LIST OF SUB-TOPICS:

• Introduction
• Thermometer
• Mercury Thermometer
• Constant Volume Gas Thermometer (CVGT)
• Constant Pressure Gas Thermometer (CPGT)
• Platinum Resistance Thermometer (PRT)
• Thermocouple
• Pyrometer
• Thermistors
• Liquid Crystal Thermometer

In last article, we have studied different temperature scales. In this article, we shall discuss methods of measurement of temperature and thermometers.

Temperature can be defined in several ways:

• The temperature may be defined as the degree of hotness or coldness of a body.
• The temperature of a body is an indicator of the average thermal energy (Kinetic energy) of the molecules of the body.
• It is that physical quantity which decides the flow of heat in bodies brought in contact. Heat always flow from the body at higher temperature to the body at the lower temperature.

It is measured in °C (centigrade or Celsius) or K (Kelvin). It is measured by a device called a thermometer. The common thermometer is a mercury thermometer.

The branch of Physics that deals with the measurement of temperature is called Thermometry.

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Thermometer:

A thermometer is an instrument used to measure temperature. It works based on the principle that certain physical properties of materials change with temperature. Thermometers typically contain a temperature-sensitive element, such as mercury, alcohol, or a thermocouple, which expands or contracts in response to temperature changes. Thermometers are widely used in various fields, including meteorology, medicine, food processing, and industrial processes, to monitor and control temperature.

Temperature is often measured with the use of a thermometer. To understand how thermometers work, one must first understand the concept of thermal equilibrium. Two bodies are said to be in thermal equilibrium with each other if no transfer of heat takes place when they are brought in contact, clearly, the two bodies are at the same temperature.

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Mercury Thermometer:

A Mercury thermometer is a type of thermometer that uses mercury as the temperature-sensitive element. Mercury thermometer work on the principle of thermal expansion of liquids. In case of mercury thermometer, mercury (liquid) expands when the temperature increases. This rise in the level of mercury in the capillary gives the temperature readings.

Elements of Mercury Thermometer:

• Mercury as the Temperature-Sensitive Element: In a mercury thermometer, the temperature-sensitive element is a column of mercury contained within a glass capillary tube. Mercury is a suitable choice for thermometers because it expands and contracts in a uniform manner with changes in temperature and it does not stick to the glass.
• Glass Capillary Tube: The thermometer consists of a sealed glass tube with a small bulb at one end and a narrow capillary tube. The capillary tube contains the mercury column, and the bulb serves as a reservoir for the mercury.

Working of Mercury Thermometer:

As the temperature increases, the mercury inside the thermometer expands and rises up the capillary tube. Conversely, when the temperature decreases, the mercury contracts and retreats back into the bulb.

Calibration:

Mercury thermometers are calibrated to provide accurate temperature readings. The glass tube is marked with a scale that correlates the height of the mercury column with specific temperature values. The scale is often marked in Celsius (°C) or Fahrenheit (°F) degrees.

Advantages of Mercury Thermometer:

Mercury thermometers have been widely used for temperature measurement in various fields for several reasons, which include the following advantages:

• Accuracy: Mercury thermometers provide accurate temperature readings over a wide range of temperatures. Mercury expands and contracts uniformly with changes in temperature, allowing for precise measurement.
• Wide Range: Mercury thermometers cover a wide temperature range from −37 to 356 °C (−35 to 673 °F); the instrument’s upper temperature range may be extended through the introduction of an inert gas such as nitrogen.
• Thermal Conductivity: Mercury has a high thermal conductivity, meaning it responds quickly to changes in temperature. This characteristic enables mercury thermometers to provide relatively fast temperature readings compared to some other types of thermometers.
• Versatility: Mercury thermometers can measure temperatures across a broad range, making them suitable for various applications in laboratories, medical settings, and industrial environments.
• Linear Expansion: Mercury expands and contracts in a linear manner with changes in temperature, making it relatively easy to calibrate mercury thermometers for accurate temperature measurement.
• Ease of Reading: Mercury is opaque and shining. It does not stick to glass-sides.  The clear glass tube and mercury column make it easy to read the temperature on a mercury thermometer. The markings on the scale are visible and straightforward to interpret.
• Longevity: When handled properly, mercury thermometers can last a long time without significant degradation in accuracy or performance.

Disadvantages of Mercury Thermometer:

While mercury thermometers are accurate and reliable, they pose potential health and environmental hazards due to the toxicity of mercury. Accidental breakage of a mercury thermometer can release mercury vapour, which is harmful if inhaled. For this reason, many countries have phased out the use of mercury thermometers in favour of safer alternatives, such as digital thermometers or alcohol-filled thermometers.

Despite safety concerns, mercury thermometers have been widely used and have played a significant role in temperature measurement in various fields. However, their use is decreasing due to environmental and health considerations, and alternative thermometer technologies are becoming more prevalent.

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Constant Volume Gas Thermometer:

A Constant Volume Gas Thermometer (CVGT), is a device used to measure temperature based on the principles of ideal gas behaviour. CVGT work on principle of Gay-Lussac’s law. Gay- Lussac’s Law states that when volume of a gas is constant, the pressure of the gas is directly proportional to its absolute temperature. As the temperature changes, the pressure changes accordingly. Measuring the pressure, temperature can be measured.

Constant volume gas thermometers are used primarily in scientific research and metrology (the science of measurement) for precise temperature measurements. They are often employed in situations where high accuracy and precision are required, such as in fundamental scientific experiments and calibration laboratories.

Construction:

The components of the apparatus are as follows:

• Container: The CVGT consists of a container with a fixed volume. This container is typically made of a material that does not react with the gas being used and can withstand high pressures and temperature changes.
• Gas: The container is filled with a gas, often a noble gas like helium or argon, at a known pressure and temperature. The gas is chosen for its inert properties and its ability to follow the ideal gas law accurately over a wide range of temperatures and pressures.
• Pressure Measurement System: A pressure measurement system is integrated into the CVGT to measure the pressure of the gas inside the container. This system may include a manometer, Bourdon gauge, or other pressure sensing devices capable of accurately measuring the pressure of the gas.
• Thermometer: A thermometer is used to measure the temperature of the gas inside the container. This thermometer may be a separate device inserted into the container or integrated directly into the CVGT.
• Sealing Mechanism: The container of the CVGT must be tightly sealed to prevent gas leaks and maintain a constant volume. The sealing mechanism may involve O-rings, gaskets, or other sealing materials capable of withstanding high pressures and temperature changes.
• Supporting Components: Various supporting components such as valves, fittings, and pressure regulators may be included in the construction of the CVGT to facilitate gas handling, pressure control, and temperature measurement.
• Calibration: The CVGT is calibrated by measuring the pressure of the gas at two known temperature points, typically at the freezing and boiling points of water under standard atmospheric pressure. These temperature-pressure data points are then used to establish a temperature-pressure relationship for the gas.

Measurement of Temperature:

Once calibrated, the CVGT can be used to measure temperatures by measuring the pressure of the gas at the temperature of interest and using the established temperature-pressure relationship to determine the corresponding temperature.

By Gay Lussac’s Law at constant volume of a gas

P α T

Thus

Where, P₁ = Initial Pressure (Known)

T₁ = Initial Absolute Temperature (Known)

P₂ = Final Pressure (To be measured)

T₂ = Final Absolute Temperature (To be calculated)

Advantages of CVGT:

CVGTs offer several advantages in temperature measurement, especially in situations where high accuracy and precision are required. Here are some of the key advantages:

• High Accuracy: CVGTs provide highly accurate temperature measurements. They operate based on the ideal gas law, which establishes a direct relationship between the pressure of the gas and the absolute temperature. This relationship allows for precise temperature determination.
• Wide Temperature Range: CVGTs can measure temperatures across a wide range, from cryogenic temperatures to very high temperatures. This versatility makes them suitable for various applications in scientific research, metrology, and industrial processes.
• Direct Measurement: CVGTs directly measure the temperature of the gas by measuring its pressure at constant volume. This direct measurement approach eliminates the need for complex conversions or corrections, leading to more straightforward and accurate temperature readings.
• Insensitive to Gas Composition: CVGTs are relatively insensitive to the composition of the gas used inside the thermometer. As long as the gas behaves ideally, its composition does not significantly affect temperature measurements, enhancing the reliability and universality of CVGTs.
• Stable Calibration: Once calibrated, CVGTs maintain stable and consistent temperature-pressure relationships over time. This stability allows for long-term use without frequent recalibration, reducing maintenance requirements and ensuring reliable temperature measurements.
• High Precision: CVGTs can achieve high precision in temperature measurement, especially when using sensitive pressure measurement devices. This precision is essential in scientific research, quality control, and other applications where precise temperature control is critical.
• Minimal Thermal Lag: CVGTs typically exhibit minimal thermal lag, meaning they respond quickly to temperature changes. This rapid response time is advantageous in dynamic temperature measurement applications and experiments requiring real-time temperature monitoring.
• Suitability for Fundamental Studies: CVGTs are often used in fundamental scientific studies and metrological applications where precise temperature measurement is essential. They provide a basis for establishing temperature scales and calibrating other temperature measurement devices.

Disadvantages of CVGT:

While Constant Volume Gas Thermometers (CVGTs) offer many advantages, they also have some notable disadvantages and limitations:

• Complexity: CVGTs can be relatively complex to construct and operate compared to simpler temperature measurement devices like liquid-in-glass thermometers or electronic thermometers. They require precise calibration and careful handling to ensure accurate temperature measurements.
• Specialized Equipment: The construction and calibration of CVGTs often require specialized equipment and expertise, making them less accessible and practical for everyday temperature measurement tasks.
• Pressure Sensitivity: CVGTs are highly sensitive to changes in pressure, which can affect the accuracy of temperature measurements. Variations in ambient pressure or pressure within the gas chamber can introduce errors in temperature readings.
• Limited Practicality: While CVGTs offer high accuracy and precision, they may not always be the most practical choice for temperature measurement in certain applications. They are typically used in laboratory settings or metrology applications where precise temperature control is required.
• Safety Concerns: Some gases used in CVGTs, such as helium or argon, can pose safety risks if mishandled or released into the environment. Additionally, the high pressures involved in CVGTs can present safety hazards if proper precautions are not taken.
• Inertia and Response Time: CVGTs may exhibit inertia and response time delays, especially when compared to more modern temperature measurement devices like electronic thermometers. This slower response time can be a limitation in applications requiring rapid temperature changes.
• Environmental Impact: The use of certain gases in CVGTs, particularly if they are released into the environment, can have environmental implications. Gases such as helium and argon are finite resources, and their extraction and use contribute to environmental impacts.
• Cost: CVGTs can be costly to manufacture, calibrate, and maintain, particularly when compared to other types of thermometers. The specialized equipment and expertise required for CVGTs can contribute to higher costs associated with their use.

While CVGTs remain important tools for precise temperature measurement in certain applications, it’s essential to consider their limitations and weigh them against the specific requirements of the measurement task at hand. In many cases, alternative temperature measurement methods may offer a more practical and cost-effective solution.

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Constant Pressure Gas Thermometer:

A Constant Pressure Gas Thermometer (CPGT), is a device used to measure temperature based on the principles of ideal gas behaviour. CPGT work on principle of Charle’s law. Charle’s Law states that when pressure of a gas is constant, the volume of the gas is directly proportional to its absolute temperature. As the temperature changes, the volume changes accordingly. Measuring the volume, temperature can be measured.

Construction:

The thermometric part consists of a silica bulb A (thermometer Bulb) connected to exactly similar bulb R through capillary tube ab. Bulb R is filled with mercury, this mercury can be drained out by operating draining knob at the bottom of bulb R.

The compensating part consists of another bulb B exactly similar bulbs A and R is connected to the system using capillary tube cd exactly similar to capillary tube ab (same length and same bore). The two capillary tubes ab and cd are always kept side by side to remain at the same temperature.

The thermometric part and the compensating part are connected to each other through manometer M.

Working:

All the three bulbs A, R, and B are kept in melting ice and ends of capillary tube are opened so that all parts of system are at atmospheric pressure. Bulb R is filled with mercury and the ends of capillary tubes are sealed and system is made air tight.

Bulb A is immersed in a bath of unknown temperature, while bulbs R and B are still maintained in melting ice. The pressure of air in bulb A increases thus there is difference in the level of mercury in the manometer M. The mercury in Bulb R is drained out by operating draining knob till the level in arms of manometer is equal again. The volume of drained mercury is measured.

Calculation

Θ = vT_o/(V-v)

Where Θ = Temperature to be measured

T_o = Temperature of air in bulbs B and R

 v = Volume of mercury taken out

V = Volume of air in each capillary tube ab and cd

Advantages of CPGT:

Constant Pressure Gas Thermometers (CPGTs) offer several advantages in temperature measurement, particularly in situations where high accuracy and stability are required. Here are some of the key advantages of CPGTs:

• High Accuracy: CPGTs provide highly accurate temperature measurements. They operate based on the principle of constant pressure gas behaviour, which allows for precise determination of temperature based on the volume of the gas.
• Stability: CPGTs maintain stable temperature-volume relationships over time. Once calibrated, they exhibit consistent and predictable responses to changes in temperature, making them reliable instruments for temperature measurement.
• Direct Measurement: CPGTs directly measure temperature based on the volume of the gas at constant pressure. This direct measurement approach eliminates the need for complex conversions or corrections, leading to more straightforward and accurate temperature readings.
• Wide Temperature Range: CPGTs can measure temperatures across a wide range, from cryogenic temperatures to very high temperatures. This versatility makes them suitable for various applications in scientific research, metrology, and industrial processes.
• Insensitivity to Gas Composition: CPGTs are relatively insensitive to the composition of the gas used inside the thermometer. As long as the gas behaves ideally, its composition does not significantly affect temperature measurements, enhancing the reliability and universality of CPGTs.
• Minimal Thermal Lag: CPGTs typically exhibit minimal thermal lag, meaning they respond quickly to temperature changes. This rapid response time is advantageous in applications requiring real-time temperature monitoring and control.
• Practicality in Controlled Environments: CPGTs are well-suited for use in controlled laboratory environments where precise temperature control is required. They offer high accuracy and stability under controlled conditions, making them valuable tools for scientific research and experimentation.
• Long-Term Stability: Once calibrated, CPGTs maintain stable temperature-volume relationships over extended periods. This long-term stability allows for continuous and reliable temperature measurement without the need for frequent recalibration.

Disadvantages of CPGT:

Constant Pressure Gas Thermometers (CPGTs) have several disadvantages and limitations despite their accuracy and stability. Some of the main disadvantages include:

• Complexity and Cost: CPGTs can be complex and expensive to construct, calibrate, and maintain. They require precise engineering and calibration procedures, as well as specialized equipment and expertise, which can increase their cost and complexity compared to other types of thermometers.
• Pressure Sensitivity: CPGTs are highly sensitive to changes in pressure, which can affect the accuracy of temperature measurements. Variations in ambient pressure or pressure within the gas chamber can introduce errors in temperature readings, requiring careful pressure control and compensation.
• Limited Practicality: While CPGTs offer high accuracy and stability, they may not always be the most practical choice for temperature measurement in certain applications. They are typically used in laboratory settings or metrology applications where precise temperature control is required, but they may not be suitable for field or industrial applications due to their complexity and cost.
• Susceptibility to Contamination: CPGTs are susceptible to contamination of the gas chamber, which can affect the accuracy and stability of temperature measurements. Contaminants such as moisture, gases, or particulate matter can introduce errors and require thorough cleaning and maintenance procedures.
• Limited Range of Gas: CPGTs are typically designed to operate with specific gases that behave ideally over a wide range of temperatures and pressures. The choice of gas can limit the temperature range and applicability of CPGTs in certain situations.
• Safety Concerns: The use of certain gases in CPGTs, such as helium or argon, can pose safety risks if mishandled or released into the environment. Additionally, the high pressures involved in CPGTs can present safety hazards if proper precautions are not taken. The vapours of mercury used is poisonous.
• Response Time: CPGTs may exhibit slower response times compared to other types of thermometers, especially in situations where rapid temperature changes occur. This slower response time can be a limitation in applications requiring real-time temperature monitoring and control.

Despite these disadvantages, CPGTs remain valuable tools for precise temperature measurement in controlled laboratory environments and metrology applications where accuracy and stability are paramount. However, it’s essential to consider their limitations and weigh them against the specific requirements of the measurement task at hand. In many cases, alternative temperature measurement methods may offer more practical and cost-effective solutions.

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Platinum Resistance Thermometer:

A Platinum Resistance Thermometer (PRT), also known as a platinum resistance temperature detector (RTD), is a type of thermometer that utilizes the change in electrical resistance of platinum wire with temperature to measure temperature accurately. The Platinum Resistance Thermometer works on the principle that the resistance of a platinum wire changes in a predictable manner as the temperature changes. Platinum is chosen for its linear resistance-temperature relationship, high stability, and repeatability over a wide temperature range.

Construction:

The construction of a Platinum Resistance Thermometer (PRT) involves several key components and considerations to ensure accurate temperature measurement. The construction of a typical PRT is as follows:

• Platinum Wire: The heart of a PRT is a fine platinum wire that exhibits a predictable change in electrical resistance with temperature variations. Platinum is chosen for its linear resistance-temperature relationship, stability, and repeatability over a wide temperature range.
• Support Structure: The platinum wire is typically wound around a support structure made of a non-conductive material, such as ceramic or glass. This support structure provides mechanical stability and protection for the platinum wire.
• Lead Wires: Electrical lead wires are attached to the platinum wire to allow for connection to a measurement circuit. The lead wires should be made of a conductive material that does not introduce significant resistance or interference.
• Encapsulation: The platinum wire and support structure are often encapsulated in a protective sheath or housing. This encapsulation helps to shield the PRT from external factors such as moisture, contaminants, and mechanical damage.
• Calibration Markers: PRTs are calibrated at specific reference temperatures to establish the relationship between resistance and temperature. Calibration markers or reference points may be added to the PRT to aid in calibration and temperature measurement.
• Terminal Connection: The terminal connection point where the lead wires are connected to the external measurement circuit is usually located on the housing or sheath of the PRT. This connection point should be securely sealed to prevent moisture ingress and ensure reliable electrical contact.
• Measurement Circuit (External): PRTs are typically used in a Wheatstone bridge circuit configuration. A known current is passed through the platinum wire, and the voltage drop across the wire is measured. The resistance of the wire, and thus the temperature, can be calculated using the voltage and the known current.

Working:

The resistance of the platinum wire changes with temperature following the Callendar-Van Dusen equation or the ITS-90 (International Temperature Scale of 1990) standard. This change is typically very linear over a wide range of temperatures, providing excellent accuracy and stability.

Once calibrated, the PRT can be used to measure temperatures by measuring the resistance of the platinum wire and using the calibration coefficients to calculate the corresponding temperature. The temperature measurement can be displayed directly on a digital thermometer or transmitted to a data acquisition system for further processing.

Advantages of PTR:

Platinum Resistance Thermometers (PRTs) offer several advantages compared to other types of temperature sensors. Here are some of the key advantages:

• High Accuracy: PRTs provide highly accurate temperature measurements over a wide range of temperatures. Platinum has a linear resistance-temperature relationship, allowing for precise and reliable temperature readings.
• Stability: PRTs offer excellent long-term stability and repeatability. The resistance-temperature characteristics of platinum are well-defined and consistent, resulting in stable and reliable temperature measurements over time.
• Wide Temperature Range: PRTs can measure temperatures ranging from cryogenic temperatures to several hundred degrees Celsius or higher. They offer a wide temperature range of operation, making them suitable for various applications across different industries.
• Linear Response: The resistance of platinum in PRTs changes linearly with temperature variations, simplifying calibration and temperature compensation processes.
• Repeatability: PRTs provide repeatable temperature measurements, allowing for consistent results in laboratory experiments, industrial processes, and other applications.
• Low Drift: PRTs exhibit minimal drift over time, ensuring that temperature measurements remain accurate and reliable over extended periods.
• High Sensitivity: Platinum has a relatively high temperature coefficient of resistance (TCR), resulting in high sensitivity to temperature changes. This high sensitivity enables PRTs to detect small temperature variations accurately.
• Interchangeability: PRTs are highly interchangeable, meaning that different PRTs of the same type can be used interchangeably without significant calibration adjustments. This interchangeability simplifies instrument calibration and maintenance procedures.
• Low Self-Heating: PRTs generate minimal self-heating when subjected to an electrical current, reducing the impact of self-heating on temperature measurements.
• Compatibility with Standardization: PRTs are widely used as reference standards in laboratories and industries due to their high accuracy, stability, and compatibility with standardization efforts such as the International Temperature Scale of 1990 (ITS-90).

Disadvantages of PRT:

While Platinum Resistance Thermometers (PRTs) offer many advantages, they also have some disadvantages and limitations. Here are some of the main drawbacks of PRTs:

• Cost: PRTs can be relatively expensive compared to other types of temperature sensors. The cost of platinum, as well as the precision manufacturing required to produce accurate PRTs, contributes to their higher price.
• Fragility: PRTs can be fragile due to their fine platinum wire construction and delicate support structures. They may be more susceptible to mechanical damage, such as bending or breaking, compared to some other types of temperature sensors.
• Slow Response Time: PRTs generally have a slower response time compared to some other temperature sensors, such as thermocouples. The time required for the platinum wire to reach thermal equilibrium with the surrounding environment can result in slower temperature response times.
• Limited Temperature Range: While PRTs can measure temperatures over a wide range, they may not be suitable for extreme temperature conditions, such as those encountered in very high-temperature industrial processes or in cryogenic applications. Extreme temperatures can affect the performance and accuracy of PRTs.
• Susceptibility to Contamination: PRTs can be sensitive to contamination of the platinum wire, which can affect their accuracy and stability. Contaminants such as moisture, gases, or particulate matter can introduce errors and require thorough cleaning and maintenance procedures.
• Electrical Excitation Required: PRTs require an external electrical excitation source to measure temperature accurately. This requirement for electrical excitation can introduce additional complexity and potential sources of error in temperature measurement systems.
• Limited Flexibility: The physical construction and design of PRTs may limit their flexibility in certain applications. They may not be as adaptable to harsh environments or space-constrained installations compared to some other types of temperature sensors.
• Calibration Requirements: PRTs require periodic calibration to maintain accurate temperature measurements over time. Calibration procedures can be time-consuming and may require specialized equipment and expertise.

Despite these disadvantages, PRTs remain widely used in many industries and applications where high accuracy, stability, and repeatability are essential for precise temperature measurement. It’s important to consider the specific requirements of each application when selecting a temperature sensor and to weigh the advantages and disadvantages of different sensor types accordingly.

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Thermocouple:

A thermocouple is a type of temperature sensor that consists of two different metal wires joined together at one end, called the junction. When there is a temperature gradient along the length of the thermocouple, it generates a voltage proportional to the temperature difference between the two ends. This phenomenon is known as the Seebeck effect.

Construction:

A thermocouple is a temperature sensor that operates based on the Seebeck effect, which describes the generation of a voltage when two dissimilar metals are joined together at a junction and there is a temperature gradient along the length of the metals.

• Metal Wires: Thermocouples consist of two different metal wires joined together at one end to form the sensing junction. The metals used in the wires determine the thermocouple type and its temperature range. Common metal combinations include chromel-alumel (Type K), iron-constantan (Type J), and copper-constantan (Type T), among others.
• Insulation: The metal wires are typically insulated from each other along their length to prevent electrical shorting. The insulation material is chosen to withstand the temperature and environmental conditions of the application.
• Protection Sheath: In many applications, the thermocouple wires are housed within a protective sheath made of stainless steel, ceramic, or other suitable materials. The sheath shields the thermocouple from mechanical damage, corrosion, and environmental factors.
• Connection Head: At the end opposite the sensing junction, the thermocouple wires are connected to a termination point, usually within a connection head. The connection head provides a secure enclosure for the wiring connections and allows for easy access for calibration and maintenance.

Working:

• Seebeck Effect: When there is a temperature gradient along the length of the two dissimilar metal wires forming the sensing junction, a voltage is generated. This voltage is proportional to the temperature difference between the sensing junction and the reference (cold) junction, usually located at or near the termination point.
• Measurement Circuit: The voltage generated by the thermocouple is measured using a voltmeter or a temperature measurement device. The voltage is typically very small, so the measurement circuit needs to be sensitive to detect it accurately. Generally wheatstone’s bridge is used.
• Cold Junction Compensation: Accurate temperature measurement with a thermocouple requires compensation for the temperature of the reference (cold) junction. Specialized circuits or techniques are used to measure the temperature at the reference junction and compensate for its effect on the thermocouple output.
• Temperature Calculation: Once the voltage generated by the thermocouple is measured and compensated for the reference junction temperature, it is converted into a temperature reading using calibration tables or equations specific to the thermocouple type and temperature range.

Overall, thermocouples are widely used temperature sensors in various industries and applications due to their wide temperature range, fast response time, durability, and simplicity of construction.

Types of Thermocouples:

Advantages of Thermocouple:

Thermocouples offer several advantages that make them widely used for temperature measurement in various industries and applications.

• Wide Temperature Range: Thermocouples can measure temperatures ranging from cryogenic temperatures to extremely high temperatures (up to around 2300°C or 4172°F), depending on the type of thermocouple and the materials used. This wide temperature range makes thermocouples suitable for a broad range of applications across different industries.
• Fast Response Time: Thermocouples have a fast response time, allowing for rapid temperature measurement and monitoring. This makes them well-suited for applications where quick temperature changes need to be detected or controlled.
• Robustness and Durability: Thermocouples are relatively robust and durable temperature sensors. They can withstand harsh environments, mechanical vibrations, and high electromagnetic interference, making them suitable for use in industrial environments and challenging conditions.
• Simple Construction: Thermocouples consist of only two wires joined together at one end, making them simple in construction and easy to install. Their simplicity makes them cost-effective and versatile for various applications.
• Wide Variety of Types and Materials: Thermocouples are available in a wide variety of types and materials, each offering different temperature ranges, accuracies, and characteristics. Common types include Type K, Type J, Type T, and Type E thermocouples, each suitable for specific temperature ranges and environments.
• Compatibility with Many Environments: Thermocouples are compatible with many different environments and can be used in various gases, liquids, and solids. They are widely used in industrial processes, HVAC systems, automotive applications, and scientific research.
• No External Power Required: Thermocouples generate their own voltage signal when subjected to a temperature gradient, eliminating the need for external power sources. This makes them suitable for remote or portable applications where power may be limited or unavailable.
• Interchangeability: Thermocouples are highly interchangeable, meaning that different thermocouples of the same type can be used interchangeably without significant calibration adjustments. This interchangeability simplifies instrument calibration and maintenance procedures.
• Cost-Effective: Thermocouples are generally more cost-effective compared to some other types of temperature sensors, such as resistance temperature detectors (RTDs) and infrared thermometers. Their simple construction, durability, and versatility contribute to their cost-effectiveness.

Overall, thermocouples offer many advantages, including wide temperature range, fast response time, robustness, simplicity, compatibility with various environments, and cost-effectiveness, making them one of the most commonly used temperature sensors in numerous industrial, commercial, and scientific applications.

Disadvantages of Thermocouple:

While thermocouples offer many advantages, they also have some disadvantages and limitations. Here are some of the key disadvantages of thermocouples:

• Non-Linear Output: The voltage output of a thermocouple is non-linear with temperature, especially over wide temperature ranges. This non-linearity can introduce errors in temperature measurements, requiring compensation and correction techniques to achieve accurate readings.
• Cold Junction Compensation: Accurate temperature measurement with thermocouples requires compensation for the temperature of the reference junction (cold junction). Specialized equipment or compensation techniques are used to account for temperature variations at the cold junction, adding complexity to temperature measurement systems.
• Limited Accuracy: While thermocouples offer good accuracy for many industrial applications, they may not be as accurate as some other temperature sensors, such as resistance temperature detectors (RTDs), especially at lower temperatures. The accuracy of thermocouples can be affected by factors such as wire quality, calibration, and environmental conditions.
• Sensitivity to Electrical Noise: Thermocouples are susceptible to electrical noise and interference, which can affect the accuracy and stability of temperature measurements. Proper shielding and grounding techniques are required to minimize the impact of electrical noise on thermocouple signals.
• Limited Resolution: Thermocouples have limited resolution compared to some other temperature sensors, such as RTDs and thermistors. The resolution of a thermocouple is determined by the sensitivity of the thermocouple and the accuracy of the measurement system.
• Limited Temperature Range for Some Types: While thermocouples offer a wide temperature range overall, some specific types of thermocouples have limited temperature ranges. For example, Type T thermocouples have a relatively narrow temperature range compared to other types, making them unsuitable for high-temperature applications.
• Susceptibility to Corrosion and Contamination: Certain environments can cause corrosion or contamination of thermocouple materials, affecting their accuracy and reliability over time. Protective sheaths or coatings may be required to protect thermocouples in corrosive or contaminating environments.
• Heterogeneity and Stability Issues: Thermocouples made from different materials may exhibit heterogeneity in their characteristics, leading to variations in temperature measurements. Additionally, thermocouples may suffer from stability issues over time, resulting in drift and changes in calibration.

Despite these disadvantages, thermocouples remain widely used for temperature measurement in various industries and applications due to their versatility, ruggedness, wide temperature range, and suitability for harsh environments. It’s important to consider the specific requirements of each application and weigh the advantages and disadvantages of different temperature sensors accordingly.

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Pyrometers:

A pyrometer is a device used to measure the temperature of objects or surfaces without making physical contact. Pyrometers work based on the principle of measuring the thermal radiation emitted by an object, which is related to its temperature according to the laws of blackbody radiation. One of the primary advantages of pyrometers is that they can measure the temperature of objects without physical contact. This is particularly useful for measuring the temperature of objects that are moving, inaccessible, or hazardous to touch. Pyrometers are used in a wide range of industrial, scientific, and commercial applications, including metal processing, glass manufacturing, ceramics, automotive, aerospace, and research laboratories. They are particularly useful for monitoring and controlling temperatures in high-temperature processes and environments

• Principle of Operation: Pyrometers measure the intensity of thermal radiation emitted by an object, usually within the infrared spectrum. The intensity of thermal radiation emitted by an object is directly related to its temperature, according to the Stefan-Boltzmann law and Planck’s law of blackbody radiation.
• Optical System: Pyrometers typically employ an optical system to focus the thermal radiation emitted by the object onto a detector. The optical system may include lenses, mirrors, or fibre optics to collect and direct the radiation to the detector.
• Detector: The detector in a pyrometer converts the incoming thermal radiation into an electrical signal. Different types of detectors may be used, including thermopiles, bolometers, and photodiodes, depending on the specific application and temperature range.
• Accuracy and Calibration: The accuracy of temperature measurements with pyrometers depends on various factors, including the calibration of the instrument, the stability of the detector, and the emissivity of the object being measured. Calibration standards and procedures are used to ensure accurate temperature measurements.

Advantages of Pyrometer:

Pyrometers offer several advantages in temperature measurement, particularly in situations where non-contact measurement and high-temperature sensing are required. Here are some key advantages of pyrometers:

• Non-contact Measurement: Pyrometers enable temperature measurement without physical contact with the object being measured. This feature is especially valuable for measuring the temperature of moving objects, fragile materials, or objects at high temperatures where contact measurement may be impractical or impossible.
• Wide Temperature Range: Pyrometers can measure temperatures ranging from low (e.g., room temperature) to extremely high temperatures (e.g., thousands of degrees Celsius). This wide temperature range makes them suitable for various industrial, scientific, and commercial applications, including metal processing, glass manufacturing, ceramics, and automotive.
• Fast Response Time: Pyrometers offer fast response times, allowing for rapid temperature measurements. This makes them ideal for applications where temperature changes need to be monitored or controlled quickly, such as industrial processes, combustion monitoring, and materials processing.
• Remote Sensing: Pyrometers can measure temperature from a distance, making them suitable for measuring objects that are difficult to access or located in hazardous environments. They are commonly used in industrial furnaces, kilns, and reactors where direct contact measurement is not feasible.
• Versatility: Pyrometers are versatile instruments that can be used in various environments and applications. They are available in different configurations, including portable handheld units, fixed-mount units, and online monitoring systems, to meet specific measurement requirements.
• Accuracy and Precision: Modern pyrometers offer high levels of accuracy and precision in temperature measurement. They employ advanced optics, detectors, and signal processing techniques to ensure accurate and reliable temperature readings across a wide range of temperatures and operating conditions.
• Durability and Reliability: Pyrometers are designed to withstand harsh industrial environments, including high temperatures, dust, humidity, and vibration. They are built with rugged enclosures, durable optics, and robust electronics to ensure long-term reliability and performance in demanding applications.
• Real-time Monitoring and Control: Pyrometers can be integrated into automated systems for real-time temperature monitoring and control. They provide valuable data for process optimization, quality control, and predictive maintenance in manufacturing and industrial processes.
• Safety: Pyrometers contribute to improved safety in industrial environments by enabling temperature measurement from a safe distance, reducing the risk of operator exposure to hazardous conditions or hot surfaces.

Thus, pyrometers offer numerous advantages in temperature measurement, including non-contact measurement, wide temperature range, fast response time, versatility, accuracy, durability, and safety. These features make them indispensable tools in a wide range of industries and applications where precise and reliable temperature measurement is essential.

Disadvantages of Pyrometers:

While pyrometers offer many advantages in temperature measurement, they also have some limitations and disadvantages.

• Emissivity Variations: Pyrometers rely on the assumption of uniform emissivity, which refers to the ability of a surface to emit thermal radiation. However, the emissivity of real-world surfaces can vary based on factors such as surface finish, material composition, and surface condition. Variations in emissivity can lead to measurement errors and inaccuracies.
• Limited Accuracy at Low Temperatures: Pyrometers may have limited accuracy at low temperatures, especially below 100°C (212°F). At lower temperatures, the emitted thermal radiation is relatively weak, making it challenging to distinguish the signal from background noise accurately.
• Distance-to-Spot Ratio: Pyrometers have a specified distance-to-spot ratio, which determines the size of the measurement area at a given distance. In applications where precise targeting is required, limitations in the distance-to-spot ratio can affect the accuracy of temperature measurements.
• Reflection and Interference: Reflections from nearby surfaces and interference from ambient light sources can affect the accuracy of pyrometer measurements. Reflected radiation can lead to errors in temperature readings, particularly in environments with shiny or reflective surfaces.
• Cost: High-quality pyrometers with advanced features and capabilities can be relatively expensive compared to other temperature measurement devices, such as thermocouples and thermistors. The cost of calibration, maintenance, and training may also contribute to the overall expense of implementing pyrometry systems.
• Calibration and Maintenance: Pyrometers require regular calibration to ensure accurate and reliable temperature measurements. Calibration procedures can be complex and time-consuming, requiring specialized equipment and trained personnel. Additionally, pyrometers may require periodic maintenance to ensure proper functionality and performance.
• Limited Temperature Range for Some Types: While pyrometers can measure a wide range of temperatures, some specific types may have limited temperature ranges. Certain pyrometer technologies may not be suitable for extremely high-temperature applications or very low-temperature measurements.
• Response Time: While pyrometers generally offer fast response times, the response time can vary depending on the type of pyrometer, measurement distance, and environmental conditions. In some applications where rapid temperature changes occur, limitations in response time may impact the accuracy of temperature measurements.
• Complexity of Operation: Some types of pyrometers, particularly those with advanced features and capabilities, may be complex to operate and require specialized training and expertise. Users need to understand the principles of operation, calibration procedures, and potential sources of error to obtain accurate temperature measurements.

Despite these disadvantages, pyrometers remain valuable tools for temperature measurement in various industries and applications where non-contact measurement, high-temperature sensing, and remote monitoring are required. It’s essential to consider the specific requirements of each application and weigh the advantages and disadvantages of pyrometers accordingly.

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Thermistors:

A thermistor thermometer is a type of thermometer that utilizes a thermistor as its temperature sensing element. Thermistors are temperature-sensitive resistors made from semiconductor materials whose electrical resistance changes significantly with temperature variations. Thermistor thermometers find applications in various industries and applications, including HVAC (heating, ventilation, and air conditioning) systems, automotive, medical devices, food processing, and environmental monitoring. They are particularly useful for applications requiring accurate and reliable temperature measurements over a relatively narrow temperature range.

Construction:

The construction of a thermistor thermometer involves the integration of a thermistor, which is a temperature-sensitive resistor made from semiconductor materials, into a measurement circuit.

• Principle of Operation: Thermistors operate based on the principle of the change in electrical resistance with temperature variations. They exhibit a negative temperature coefficient (NTC) or positive temperature coefficient (PTC) depending on the type of thermistor. NTC thermistors have decreasing resistance with increasing temperature, while PTC thermistors have increasing resistance with increasing temperature.
• Thermistor: The core component of a thermistor thermometer is the thermistor itself. Thermistors are typically made from semiconductor materials such as metal oxides (e.g., nickel, manganese, cobalt), which exhibit a predictable change in resistance with temperature variations. The choice of thermistor type (e.g., NTC or PTC) depends on the specific application requirements.
• Housing: The thermistor is housed within a protective casing or probe to shield it from environmental factors and physical damage. The housing material is selected to withstand the operating conditions of the application, including temperature, humidity, and chemical exposure.
• Wiring: The thermistor is connected to the measurement circuit using electrical wiring. The wiring should be of sufficient quality and gauge to minimize resistance and signal loss.
• Measurement Circuit: The measurement circuit comprises components such as resistors, capacitors, operational amplifiers, and possibly microcontrollers or integrated circuits (ICs) for signal processing and data display. The circuit is designed to measure the resistance of the thermistor accurately and convert it into a temperature reading.
• Voltage Source: A voltage source is typically provided to supply power to the measurement circuit and thermistor. The voltage source may be a battery, power supply, or integrated power management circuit, depending on the application requirements.
• Calibration Components: Calibration components, such as precision resistors and trim pots, may be included in the measurement circuit to calibrate the thermometer and ensure accurate temperature readings. Calibration is essential to account for variations in thermistor characteristics and circuit performance.
• Display and Output: The temperature reading obtained from the measurement circuit is displayed to the user through a digital display (e.g., LCD or LED) or analog gauge. Some thermistor thermometers may also include output options such as analog voltage output, serial communication (e.g., UART), or digital protocols (e.g., I2C, SPI) for interfacing with external devices or data logging systems.
• Enclosure: The entire thermometer assembly, including the measurement circuit, display, and wiring, may be enclosed within a protective housing or casing. The enclosure provides physical protection, electrical insulation, and mounting options for the thermometer.
• User Interface: Depending on the thermometer’s design and intended use, it may include user interface elements such as buttons, switches, or touchscreens for setting parameters, adjusting settings, or accessing additional features.

The construction of a thermistor thermometer can vary depending on factors such as the thermometer’s intended application, accuracy requirements, environmental conditions, and cost considerations. However, the basic principles outlined above form the foundation of most thermistor thermometer designs.

Advantages of Thermistor Thermometers:

Thermistor thermometers offer several advantages in temperature measurement, particularly in applications where high sensitivity, accuracy, and precision are required. Here are some key advantages of thermistor thermometers:

• High Sensitivity: Thermistors exhibit high sensitivity to temperature changes, making them capable of detecting even small variations in temperature. This high sensitivity allows for precise temperature measurements in a wide range of applications.
• Wide Temperature Range: Thermistor thermometers can measure temperatures across a broad range, from cryogenic temperatures to elevated temperatures. Different types of thermistors, such as negative temperature coefficient (NTC) and positive temperature coefficient (PTC) thermistors, offer temperature measurement capabilities over different ranges, providing versatility in various applications.
• Linearity: Thermistors often exhibit a linear relationship between resistance and temperature over a specific temperature range, simplifying calibration and temperature measurement calculations. This linearity enhances accuracy and precision in temperature measurement compared to some other temperature sensors.
• Fast Response Time: Thermistors have a fast response time, allowing for rapid temperature measurement and monitoring. This feature is particularly useful in applications where quick temperature changes need to be detected or controlled.
• Small Size: Thermistors are compact and lightweight, making them suitable for integration into small, space-constrained devices and systems. Their small size allows for easy installation and integration into various electronic devices and equipment.
• Low Cost: Thermistors are relatively inexpensive compared to some other temperature sensors, such as resistance temperature detectors (RTDs) and thermocouples. Their low cost makes them an economical choice for temperature measurement in many applications.
• Stability and Long-Term Reliability: Thermistors exhibit stable and consistent performance over time, with minimal drift in resistance and temperature measurement accuracy. This stability ensures long-term reliability and repeatability in temperature measurements, reducing the need for frequent calibration and maintenance.
• Low Power Consumption: Thermistors have low power consumption, making them energy-efficient and suitable for battery-powered applications and portable devices. Their low power requirements contribute to extended battery life and reduced operating costs.
• Ease of Interfacing: Thermistors can be easily interfaced with electronic circuits and microcontrollers for temperature measurement and control. Their simple electrical characteristics and predictable behaviour simplify circuit design and integration into electronic systems.
• Compatibility with Semiconductor Processes: Thermistors are semiconductor devices and are compatible with semiconductor manufacturing processes, allowing for cost-effective production and customization for specific application requirements.

Thus, thermistor thermometers offer several advantages, including high sensitivity, wide temperature range, linearity, fast response time, small size, low cost, stability, low power consumption, ease of interfacing, and compatibility with semiconductor processes. These features make them valuable temperature sensors in various industrial, commercial, and consumer applications where accurate and reliable temperature measurement is essential.

Disadvantages of Thermistor Thermometer:

Thermistors, while offering many advantages in temperature measurement, also have some limitations and disadvantages. Here are some of the key disadvantages of thermistors:

• Non-linearity: One significant drawback of thermistors is their non-linear resistance-temperature relationship. Unlike some other temperature sensors like resistance temperature detectors (RTDs), the resistance of a thermistor does not change linearly with temperature. This non-linearity can complicate calibration and temperature measurement calculations, requiring curve fitting or lookup tables for accurate temperature readings.
• Limited Temperature Range: Thermistors have a limited temperature range compared to some other temperature sensors, such as thermocouples. While they are suitable for many applications, thermistors may not be appropriate for extremely high-temperature measurements or cryogenic temperatures.
• Self-Heating: Thermistors exhibit self-heating when current passes through them to measure temperature. This self-heating effect can lead to inaccuracies in temperature measurements, especially at low currents or when high precision is required. Careful consideration and compensation techniques may be necessary to mitigate the impact of self-heating on temperature readings.
• Stability and Drift: Thermistors may exhibit stability issues and long-term drift in resistance over time. Factors such as aging, environmental conditions (e.g., temperature, humidity), and mechanical stress can contribute to changes in thermistor characteristics and performance. Regular calibration and maintenance may be required to ensure consistent and reliable temperature measurements.
• Limited Interchangeability: Thermistors are not as interchangeable as some other temperature sensors, such as thermocouples and RTDs. Each thermistor has unique characteristics, including resistance-temperature curves and tolerances, which can vary between different thermistors even of the same type and model. This lack of interchangeability can complicate replacement and calibration processes.
• Sensitivity to Overvoltage and Transients: Thermistors are sensitive to overvoltage and transient voltage spikes, which can damage or degrade their performance. Proper voltage protection measures, such as transient voltage suppressors (TVS diodes) and voltage regulators, may be necessary to safeguard thermistors from electrical overstress.
• Limited Availability of Standardized Models: Unlike some other temperature sensors, such as thermocouples and RTDs, thermistors may have limited availability of standardized models with well-defined specifications and calibration standards. This can make it challenging to select and integrate thermistors into temperature measurement systems, especially in critical or regulated applications.

Despite these disadvantages, thermistors remain widely used for temperature measurement in various industrial, commercial, and consumer applications due to their high sensitivity, low cost, compact size, and ease of integration. It’s important to consider the specific requirements and limitations of thermistors when selecting temperature sensors for different applications.

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Liquid Crystal Thermometer:

Liquid crystal thermometers, also known as liquid crystal temperature strips or liquid crystal thermochromic devices, are temperature-sensitive devices that use liquid crystal materials to display temperature information. Here’s an overview of liquid crystal thermometers:

Construction:

• Liquid Crystal Material: The core component of a liquid crystal thermometer is the liquid crystal material itself. Liquid crystals are organic compounds that exhibit changes in color or opacity in response to changes in temperature. These changes occur due to alterations in the molecular arrangement of the liquid crystal material as temperature changes.
• Substrate: The liquid crystal material is typically encapsulated within a thin, transparent plastic or polyester substrate. This substrate serves as a protective layer and provides support for the liquid crystal material.
• Adhesive Backing: Many liquid crystal thermometers feature an adhesive backing on one side of the substrate, allowing them to be affixed to various surfaces, such as containers, windows, or equipment.

Working Principle:

• Temperature Sensitivity: Liquid crystal thermometers utilize the temperature sensitivity of liquid crystal materials. As the temperature changes, the liquid crystal molecules reorient themselves, causing changes in the material’s optical properties, such as color or opacity.
• Colour Change: Liquid crystal thermometers typically feature a color scale printed on the substrate adjacent to the liquid crystal material. As the temperature changes, the liquid crystal material changes colour according to the temperature scale, providing a visual indication of the current temperature.
• Visual Observation: Users can visually observe the colour changes in the liquid crystal material to determine the approximate temperature. The colours may indicate temperature ranges or specific temperature values, depending on the design of the thermometer.

Advantages of Liquid Crystal Thermometers:

• Non-Invasive Measurement: Liquid crystal thermometers offer non-invasive temperature measurement, requiring no direct contact with the object or surface being measured. This feature is particularly useful for applications where contact measurement methods are impractical or undesirable.
• Quick Response Time: Liquid crystal thermometers have a fast response time, allowing users to quickly assess temperature changes. The colour changes in the liquid crystal material occur almost instantly in response to temperature variations.
• Compact and Portable: Liquid crystal thermometers are lightweight, compact, and portable, making them easy to transport and use in various settings. They are particularly convenient for field measurements or mobile applications.
• Low Cost: Liquid crystal thermometers are generally inexpensive compared to some other temperature measurement devices, such as digital thermometers or infrared thermometers. They offer a cost-effective solution for temperature monitoring and measurement.
• Visual Readout: Liquid crystal thermometers provide a visual readout of temperature information, eliminating the need for power sources or electronic displays. This simplicity makes them easy to use and understand, even for individuals without technical expertise.

Disadvantages of Liquid Crystal Thermometers:

• Limited Precision: Liquid crystal thermometers may provide only approximate temperature measurements and are typically less precise than digital thermometers or thermocouples.
• Temperature Range: The temperature range of liquid crystal thermometers may be limited compared to other temperature measurement devices. They may not be suitable for extreme temperature conditions or high-precision applications.
• Subject to Environmental Factors: Liquid crystal thermometers can be affected by environmental factors such as humidity, sunlight, and ambient temperature variations, which may impact their accuracy and performance.

Applications:

Liquid crystal thermometers are commonly used in various applications, including home temperature monitoring, medical diagnostics, aquariums, and educational settings. They provide a simple and convenient method for assessing temperature changes in a wide range of environments

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Conclusion:

Temperature is measured using various types of temperature sensors and instruments, each with its own principles of operation, advantages, and limitations. Each temperature measurement method has its own advantages, limitations, and application-specific considerations. The choice of temperature sensor or instrument depends on factors such as the temperature range, accuracy requirements, response time, environmental conditions, and specific application needs.

The post Measurement of Temperature appeared first on The Fact Factor.

In last article, we have studied the concept of temperature. In this article, we shall discuss different thermodynamic or temperature scales.

Temperature can be defined in several ways:

• The temperature may be defined as the degree of hotness or coldness of a body.
• The temperature of a body is an indicator of the average thermal energy (Kinetic energy) of the molecules of the body.
• It is that physical quantity which decides the flow of heat in bodies brought in contact. Heat always flow from the body at higher temperature to the body at the lower temperature.

It is measured in °C (centigrade or Celsius) or K (Kelvin). It is measured by a device called a thermometer. The common thermometer is a mercury thermometer.

The branch of Physics that deals with the measurement of temperature is called Thermometry.

Concept of Thermal Equilibrium:

Two bodies are said to be in thermal equilibrium with each other if no transfer of heat takes place when they are brought in contact, clearly, the two bodies are at the same temperature.

Characteristics of Thermal Equilibrium:

When two or more bodies are kept in contact and they are at the same temperature and there is no transfer of heat taking place between them, then those bodies are said to be in thermal equilibrium with each other. If thermal equilibrium does not exist, then heat flows from a body at a higher temperature to the body at a lower temperature, till thermal equilibrium is established.  Characteristics define thermal equilibrium are as follows:

• Equal Temperatures: In thermal equilibrium, all objects or systems involved have the same temperature. Temperature is a measure of the average kinetic energy of the particles within a substance. When objects are in thermal equilibrium, their average kinetic energies are the same.
• No Net Heat Transfer: In thermal equilibrium, there is no net transfer of heat between the objects or systems. Thus, there is no heat transfer between the bodies due to conduction or convection. This means that while individual particles may still exchange energy through collisions, the overall transfer of thermal energy between the objects results in no net change in their temperatures.
• Stable State: Thermal equilibrium represents a stable state in which the thermal properties of the objects or systems involved remain constant over time. Any initial differences in temperature between the objects or systems will eventually lead to thermal equilibrium as heat is transferred between them.
• Zero Temperature Gradient: A temperature gradient refers to the change in temperature over a distance. In thermal equilibrium, there is no temperature gradient between the objects or systems. This means that the temperature is uniform throughout the system.
• Dynamic Equilibrium: While there is no net transfer of thermal energy in thermal equilibrium, individual particles within the system may still be in motion, exchanging energy through collisions. Thermal equilibrium represents a dynamic balance where the rates of energy transfer between particles are equal.

Understanding thermal equilibrium is crucial in various fields such as thermodynamics, heat transfer, and the study of thermal properties of materials. It helps in analyzing and predicting the behaviour of systems where heat exchange is involved.

Zeroth Law of Thermodynamics:

The Zeroth Law of Thermodynamics is one of the fundamental principles that govern thermodynamic systems. It was formulated after the First and Second Laws of Thermodynamics, but its importance in establishing temperature measurement and the concept of thermal equilibrium led to its designation as the “Zeroth” law. This law introduces the concept of hotness and coldness which leads to the concept of the temperature of a body.

The Zeroth Law states that “If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.”

Thus, if two bodies P and Q are in thermal equilibrium and also P and R in thermal equilibrium then Q and R, are also in thermal equilibrium.

The Zeroth Law essentially establishes the concept of temperature and allows us to define and measure it. It provides a basis for the construction of thermometers and temperature scales. For instance, if two objects are in thermal equilibrium, they have the same temperature.

The importance of the Zeroth Law lies in its role in defining the concept of temperature and establishing the foundation for thermal equilibrium. It allows us to compare temperatures and define scales, which are fundamental for understanding and analyzing the behaviour of thermodynamic systems.

Triple Point of Water:

Phase diagram of water consists of three curves sublimation curve, evaporation curve and melting curve meeting each other at a point called the triple point. Due to these curves, the phase diagram has three regions

The region to the left of the melting curve and above the sublimation curve represents the solid phase of water i.e. ice. The region to the right of the melting curve and above the evaporation curve represents the liquid phase of water i.e. water. The region below the sublimation curve and evaporation curve represent the gaseous phase of water i.e. vapours.

A curve on the phase diagram represents the boundary between two phases of the two substances. Along any curve, the two phases can coexist in equilibrium.

Along the melting curve, ice and water can remain in equilibrium. This curve is called a fusion curve or ice line. This curve indicates that the melting point of ice decreases with an increase in pressure. Along the evaporation curve, water vapours and water can remain in equilibrium. This curve is called the vaporisation curve or steam line. This curve indicates that the boiling point of water increases with an increase in pressure. Along the sublimation curve, ice and water vapours can remain in equilibrium. This curve is called the sublimation line or hoar frost line.

The three curves meet each other at a single point at A. This common point is known as the triple point of water. At the triple point of water can coexist in all the three states in equilibrium. The triple point of water corresponds to a pressure of 0.006023 atmospheres and temperature (0.01 °C) 273.16 K.

Significance of Triple Point of Water:

• Triple point temperature of the water is the temperature at which water can coexist in all the three states viz. Ice (solid), water (liquid), vapours (gas) in equilibrium.
• This triple point temperature of the water is used for defining the absolute temperature scale. In absolute or Kelvin scale 0 K is considered as the lower fixed point while the triple point temperature of the water is taken as the upper fixed point.
• Thus one kelvin temperature corresponds to 1/273.16 of the triple point temperature.

Various Temperature Scales:

There are several temperature scales used around the world, each with its own reference points and units of measurement. Here are the most common temperature scales:

Celsius Scale (° C):

In this scale, the melting point of ice at one-atmosphere pressure and at mean sea level is taken as the lower reference point and consider as 0° C. While boiling point of water at one atmosphere pressure and at mean sea level is taken as an upper reference point and consider as 100° C. The range between the two reference points is divided into 100 equal parts and each part is called 1° C (one degree Celsius). This scale is also called a centigrade scale.

A lower limit of 0° C is considered arbitrary, this scale can be extended to indicate negative temperatures also. A temperature below -273.15° C is not possible.

Fahrenheit Scale (° F):

In this scale, the melting point of ice at one-atmosphere pressure and at mean sea level is taken as the lower reference point and consider as 32° F. While boiling point of water at one atmosphere pressure and at mean sea level is taken as the upper reference point and consider as 212° F. The range between the two reference points is divided into 180 equal parts and each part is called 1° F (one degree Fahrenheit). Nowadays, this scale is not in use.

Kelvin Scale (K):

In this scale, the lowest possible temperature -273.15° C  is taken as a lower reference point. This temperature is called absolute zero. The division of 1 K is equal to 1° C. The unit of temperature in the kelvin scale is K (kelvin) and is considered as the fundamental unit in the S.I. system of units.

Reaumer Scale:

In this scale, the melting point of ice at one-atmosphere pressure and at mean sea level is taken as the lower reference point and consider as 0° R. While boiling point of water at one-atmosphere pressure and at mean sea level is taken as an upper reference point and consider as 80° R. The range between the two reference points is divided into 80 equal parts and each part is called 1° R (one-degree Reaumer).

Conversion of Temperature in Different Scales:

Celsius scale to Kelvin scale  ° C  +  273 = K

Kelvin scale to Celsius scale  K  –  273 = ° C

Numerical Problems:

Example 01:

Find the temperature at which the temperature scales in the following pairs give the same reading: (1) Celsius and Fahrenheit and (2) Fahrenheit and Kelvin

(1) Celsius and Fahrenheit

Solution:

Let θ be the required temperature, such that F = C = θ .

We have

∴ (θ – 32)/180 = θ /100

∴ 100θ – 3200 = 180 θ

∴ – 80θ = 3200

∴ θ = – 40^oF = – 40^oC

Ans: Thus at – 40^oC or – 40^oF, the temperature scales in Celsius and Fahrenheit give the same reading.

(2) Fahrenheit and kelvin:

Solution:

Let θ be the required temperature, such that F = K = θ .

We have

∴ (θ – 32)/9 = ( θ – 273)/5

∴ 5θ – 160 = 9 θ – 2457

∴ 4θ = 2297

∴ θ = 574.25^oF = 574.25 K

Ans: Thus at 574.25^oF or 574.25^oK, the temperature scales in Fahrenheit and Kelvin give the same reading.

Example 02:

Determine the temperature on the Fahrenheit scale which is indicated by double the number on the Centigrade scale.

Solution:

Let θ be the required temperature in centigrade scale, such that C = θ and F = 2 θ .

We have

∴ (2 θ – 32)/180 = θ /100

∴ 200 θ – 3200 = 180 θ

∴ 20 θ = 3200

∴ θ = 160^oC

∴ 2 θ = 2 x 160^o = 320 ^oF

Ans: 320 ^oF is the temperature on the Fahrenheit scale which is indicated by double the number on the Centigrade scale (160^oC).

Example 03:

Convert the following temperature in centigrade into Fahrenheit

• -37 ^oC

Given C = -37 ^oC

∴ (F – 32)/180 = (-37)/100

∴ 100F – 3200 = 6660

∴ 100F = 9860

∴ F = 98.6^oF

Ans: Thus equivalent of temperature -37 ^oC is 98.6 ^oF

• 100^oC

Given C = -100 ^oC

∴ (F – 32)/180 = 100/100

∴ (F – 32)/180 = 1

∴ F – 32 = 180

∴ F = 212^oF

Ans: Thus equivalent of temperature 100 ^oF is 212 ^oF

• -192 ^oC

Given C = -192 ^oC

∴ (F – 32)/180 = (-192)/100

∴ 100F – 3200 = – 34560

∴ 100F = – 31360

∴ F = – 313.6^oF

Ans: Thus equivalent of temperature -192 ^oC is – 313.6 ^oF

Example 04:

Convert the following temperature in centigrade into Fahrenheit

• -108

Given F = -108 ^oF

∴ (-108 – 32)/180 = C/100

∴ -140/180 = C/100

∴ C = (7/9) x 100

∴ C = – 77.78 ^oC

Ans: Thus equivalent of temperature -108 ^oF is – 77.78 ^oC

• 176

Given F = 176 ^oF

∴ (176 – 32)/180 = C/100

∴ 144/180 = C/100

∴ C = (4/5) x 100

∴ C = 80 ^oC

Ans: Thus equivalent of temperature 176 ^oF is 80 ^oC

• 140

Given F = 140 ^oF

∴ (140 – 32)/180 = C/100

∴ 108/180 = C/100

∴ C = (3/5) x 100

∴ C = 60 ^oC

Ans: Thus equivalent of temperature 140 ^oF is 60 ^oC

Example 05:

The fundamental interval of a thermometer is arbitrarily divided into 80 divisions. The lower fixed point of the thermometer is marked 10 ^o. Find what reading this thermometer will show when the reading on a centigrade thermometer is 60 ^oC.

Solution:

Scale 1: Number of Divisions = n = 80, the lower Fixed Point = L = 10^o.

Centigrade Scale: Number of divisions = n = 100, the lower fixed point = L = 0^o.

Given C = 60^oC

∴ ( θ – 10)/4 = 60/5

∴ ( θ – 10)/4 = 12

∴ ( θ – 10) = 48

∴ θ = 58^o on the new scale

Ans: Thus equivalent of temperature 60 ^oC is 58^o on the new scale.

Example 06:

The lower fixed point of a thermometer is marked 10^o and the upper fixed point is 130^o, the interval between the fixed points is divided into 120 equal divisions. What should be the reading indicated by this thermometer when a Centigrade thermometer reads 40^o?

Solution:

Scale 1: Number of Divisions = n = 120, the lower Fixed Point = L = 10^o., The upper fixed point = U = 130^o

Centigrade Scale: Number of divisions = n = 100, the lower fixed point = L = 0^o.

Given C = 60^oC

∴ ( θ – 10)/6 = 40/5

∴ ( θ – 10)/6 = 8

∴ ( θ – 10) = 48

∴ θ = 58^o on the new scale

Ans: Thus equivalent of temperature 40 ^oC, is = 58^o on the new scale.

Example 07:

The fundamental interval of a thermometer is divided arbitrarily into 40 equal parts and that of another thermometer 𝑦 into 80 equal parts. If the freezing point is marked 20^o and that of y is marked 10^o, what is the temperature on when y indicates 70^o? What is the temperature in degrees celsius?

Part I:

Solution:

Scale of thermometer x: Number of Divisions = n = 40, the lower Fixed Point = L = 20^o,

Scale of thermometer y: Number of divisions = n = 80, the lower fixed point = L = 0^o.

Given Y = 70^oC

∴ (X – 20)/40 = 70/80

∴ X – 20 = 35

∴ X = 55^o on the scale of thermometer X.

Ans: Thus equivalent of temperature 70 ^o on scale of thermometer y, is = 55^o on the scale of thermometer x.

Part II:

Solution:

Scale on thermometer y: Number of Divisions = n = 80, the lower Fixed Point = L = 0^o.

Centigrade Scale: Number of divisions = n = 100, the lower fixed point = L = 0^o.

Given Y = 70^oC

∴ 70/4 = C/5

∴ C = (70/4) x 5 = 87.5^oC

Ans: Thus equivalent of temperature 70 ^o on the scale of thermometer y, is = 87.5^oC on the centigrade scale.

Example 08:

Two arbitrary scales A and B have triple points of water defined on 200 A and 350 B. What is the relation between T_A and T_B?

Solution:

The triple point of water is 373 K

For Scale A, 273 K = 200 A i.e. 1 K = (273/200) T_A …………… (1)

For Scale B, 273 K = 350 B i.e. 1 K = (273/350) T_B …………… (2)

From relations (1) and (2) we have

(273/200) T_A = (273/350) T_B

∴ 350 T_A = 200 T_B

∴ T_A / T_B = 200/350

∴ T_A / T_B = 4/7

Ans: T_A / T_B = 4/7

Example 09:

A Centigrade thermometer has its lower and upper fixed points marked – 0.5 ^oC and 100.5 ^oC. What is the true temperature when this thermometer reads30^oC? The bore of the thermometer is uniform.

Solution:

Scale 1: The lower Fixed Point = L = – 0.5 ^oC., the upper fixed point = U = 100.5 ^oC

Centigrade scale: Number of divisions = n = 100, the lower fixed point = L = 0^o.

Given S = 30^oC

∴ (30 + 0.5)/101= C/100

∴ C = (30.5/101) x 100

∴ C = 30.198^oC

Ans: Thus true temperature reading is 30.198^oC

Example 10:

A thermometer is fixed points marked as 5 and 95. What is the correct temperature in Celsius when the thermometer reads 59?

Solution:

Scale 1: The lower Fixed Point = L = 5, the upper fixed point = U = 95

Centigrade scale: Number of divisions = n = 100, the lower fixed point = L = 0^o.

Given S = 59

∴ (59 – 5)/90= C/100

∴ C = (54/90) x 100

∴ C = 60^oC

Ans: Thus correct temperature reading is 60^oC

Example 11:

In an arbitrary scale of temperature, water boils a 40 ^oC and boils at 290 ^oC. Find the boiling point of water in this scale if it boils at 62 ^oC.

Solution:

Scale 1: The lower Fixed Point = L = 40 ^oC, the upper fixed point = U = 290 ^oC

Centigrade scale: Number of divisions = n = 100, the lower fixed point = L = 0^o.

Given C = 62^oC

∴ (S – 40)/250 = 62/100

∴ S – 40 = 0.62 x 250

∴ S – 40 = 155

∴ S = 195 ^oC

Ans: Thus the boiling point of water, in the new scale is 195^oC

Example 12:

The distance between the upper and lower fixed point is 80 cm. Find the temperature on the Celsius scale if the mercury level rises to a height 10.4 cm above the lower fixed point.

Scale 1: The lower Fixed Point = L = 0 cm, the upper fixed point = U = 80 cm

Centigrade scale: Number of divisions = n = 100, the lower fixed point = L = 0^o.

Given S = 10.4 cm

∴ 10.4/80 = C/100

∴ 80C = 1040

∴ C = 1040/80 = 13 ^oC

Ans: Thus the temperature on the Celsius scale is 13 ^oC

Example 13:

The temperature of the two bodies differs by 1oC. How much do they differ on the Fahrenheit scale?

Solution:

Differentiating both sides w.r.t. temperature T

Ans: Thus the difference of 1^oC in Celsius scale corresponds to the difference of 1.8oF on the Fahrenheit scale.

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In last article we have discussed concept of heat. In this article, we shall study the concept of temperature, different temperature scales, and convert temperature in different temperature scales.

Defining Temperature:

Temperature can be defined in several ways:

• The temperature may be defined as the degree of hotness or coldness of a body.
• It is an indicator of the average thermal energy (Kinetic energy) of the molecules of the body.
• It is that physical quantity which decides the flow of heat in bodies brought in contact. Heat always flow from the body at higher temperature to the body at the lower temperature.

It is measured in °C (centigrade or Celsius) or K (Kelvin). It is measured by a device called a thermometer.

Kinetic Interpretation of Temperature:

Temperature reflects the average kinetic energy of particles in a substance. The kinetic energy of a particle is the energy associated with its motion. According to the kinetic theory:

• Temperature and Kinetic Energy: As the temperature of a substance increases, the average kinetic energy of its particles also increases. This means that at higher temperatures, the particles move faster on average.
• Temperature and Particle Speed: Temperature is directly related to the average speed of the particles in a substance. Higher temperatures correspond to higher average speeds, while lower temperatures correspond to lower average speeds.
• Collisions and Pressure: The kinetic theory also explains pressure in terms of particle motion. When particles collide with the walls of their container, they exert a force, resulting in pressure. The force of the collisions depends on the speed of the particles, which in turn is related to temperature.
• Absolute Zero: According to the kinetic theory, at absolute zero (0 Kelvin), particles would have minimal kinetic energy, meaning they would completely cease their motion. This is the lowest possible temperature and represents the point at which particles have minimal energy.

Thus, the kinetic interpretation of temperature provides a fundamental understanding of how the motion of particles at the microscopic level influences the macroscopic properties of a substance, such as its temperature, pressure, and volume.

Various Temperature Scales:

There are several temperature scales used around the world, each with its own reference points and units of measurement. Here are the most common temperature scales:

Celsius Scale (° C):

In this scale, the melting point of ice at one-atmosphere pressure and at mean sea level is taken as the lower reference point and consider as 0° C. While boiling point of water at one atmosphere pressure and at mean sea level is taken as an upper reference point and consider as 100° C. The range between the two reference points is divided into 100 equal parts and each part is called 1° C (one degree Celsius). This scale is also called a centigrade scale.

A lower limit of 0° C is considered arbitrary, this scale can be extended to indicate negative temperatures also. A temperature below -273.15° C is not possible.

Fahrenheit Scale (° F):

In this scale, the melting point of ice at one-atmosphere pressure and at mean sea level is taken as the lower reference point and consider as 32° F. While boiling point of water at one atmosphere pressure and at mean sea level is taken as the upper reference point and consider as 212° F. The range between the two reference points is divided into 180 equal parts and each part is called 1° F (one degree Fahrenheit). Nowadays, this scale is not in use.

Kelvin Scale (K):

In this scale, the lowest possible temperature -273.15° C  is taken as a lower reference point. This temperature is called absolute zero. The division of 1 K is equal to 1° C. The unit of temperature in the kelvin scale is K (kelvin) and is considered as the fundamental unit in the S.I. system of units.

Reaumer Scale:

In this scale, the melting point of ice at one-atmosphere pressure and at mean sea level is taken as the lower reference point and consider as 0° R. While boiling point of water at one-atmosphere pressure and at mean sea level is taken as an upper reference point and consider as 80° R. The range between the two reference points is divided into 80 equal parts and each part is called 1° R (one-degree Reaumer).

Difference between Heat and Temperature:

Heat and temperature are related concepts in thermodynamics, but they represent different aspects of thermal energy.

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In this article, we shall study the factors affecting the rate of a chemical reaction and the Arrhenius equation.

Factors Affecting the Rate Of Reaction:

The Concentration of Reactants:

The number of collisions and hence the activated collisions between the reactant molecules increase with the increase in concentration. According to the collision theory, the rate of a reaction should increase with the increase in the concentration since the rate is directly proportional to the collision frequency.

Pressure:

The number of collisions increases with an increase in the partial pressures of gases. Hence the rate of a reaction involving gaseous reactants increases with an increase in partial pressures. However, it has no effect on reactions involving reactants in liquid or solid phases.

It is important to keep in mind that the partial pressures of reactants can be increased by increasing the pressure of the overall system. However, the partial pressures do not increase when an inert gas or a non-reacting gas is added to the reaction mixture at constant volume.

Temperature:

The average kinetic energy increases with increase in absolute temperature. Hence the number of molecules with energy greater than the threshold energy also increases.

As a result, the number of effective collisions between reactant molecules also increases. Therefore, usually, it is observed that the rate of reaction increases with increase in temperature.

Catalyst:

The catalyst is a substance which changes the rate of a reaction without being consumed or without undergoing any chemical change during the reaction.

In case of reversible reactions, the catalyst lowers the activation energies of both forward and backward reactions to the same extent and helps in attaining the equilibrium quickly.

Some substances may decrease the rate of a reaction. These are generally referred to as negative catalysts or inhibitors. They interfere with the reaction by forming relatively stable complexes, which require more energy to break up. Thus the speed of the reaction is reduced.

Nature of Reactants:

The rate of a reaction depends on the nature of bonding in the reactants. Usually, the ionic compounds react faster than covalent compounds.

The reactions between ionic compounds in water occur very fast as they involve the only exchange of ions, which were already separated in aqueous solutions during their dissolution.

Whereas, the reactions between covalent compounds take place slowly because they require energy for the cleavage of existing bonds.

The Orientation of Reacting Species:

The reaction between the reactants occurs only when they collide in the correct orientation in space. Greater the probability of collisions between the reactants with proper orientation, greater is the rate of reaction.

The orientation of molecules affects the probability factor, p. The simple molecules have more ways of proper orientations to collide. Hence their probability factor is higher than that of complex molecules.

The orientation factor also affects the interaction between reactants and catalysts. For example in case of biological reactions, which are catalyzed by enzymes, the biocatalysts. The enzymes activate the reactant molecules (or substrates) at a particular site on them. These sites are called active sites and have definite shape and size. The size, stereochemistry, and orientation of substrates must be such that they can fit into the active site of the enzyme. Then only the reaction will proceed. This is also known as lock and key mechanism. The enzymes lose their activity upon heating or changing the pH or adding certain chemical reagents. This is due to deformation of the configuration of the active site.

Surface Area of Reactant:

The rate of a reaction increases with increase in the surface area of solid reactant if any used. The surface of a solid can be increased by grinding it to a fine powder.

This is also true with the solid catalysts, which are usually employed in finely powdered form while carrying out a chemical reaction.

The Intensity of Light:

The rate of some photochemical reactions, which occur in presence of light, increases with increase in the intensity of suitable light used.

With the increase in the intensity, the number of photons in light also increases. Hence number of reactant molecules get energy by absorbing more number of photons and undergo a chemical change.

Nature of Solvent:

The solvent may affect the rate in many ways as explained below:

The solvents are used to dissolve the reactants and while doing so they help in providing more interactive surface between reactant molecules which may be otherwise in different phases or strongly bonded in the solid phase.

Usually, solvents help in breaking the cohesive forces between ions or molecules in the solid state. The polar molecules tend to dissolve more in polar solvents with more dielectric constants and react faster in them. Whereas nonpolar molecules prefer nonpolar solvents.

In case of diffusion controlled reactions, the viscosity of the solvent plays a major role. The rate decreases with increase in the viscosity of the solvent.

Effect of Change of Temperature on the Rate of Reaction:

The average kinetic energy increases with increase in absolute temperature. Hence the number of molecules with energy greater than the threshold energy also increases.

As a result, the number of effective collisions between reactant molecules also increases. Therefore, usually, it is observed that the rate of reaction increases with increase in temperature.

The two distribution graphs are shown below for a lower temperature T₁ and a higher temperature T₂. The area under each curve represents the total number of molecules whose energies fall within the particular range.

The shaded regions indicate the number of molecules which are sufficiently energetic to meet the requirements dictated by the two values of E_a that are shown.

It is clear from these graphs that the fraction of molecules whose kinetic energy exceeds the activation energy increases quite rapidly as the temperature is raised. This the reason that virtually all chemical reactions (and all elementary reactions) proceed more rapidly at higher temperatures.

Arrhenius Equation:

Arrhenius came up with an equation that demonstrated that rate constants of different kinds of chemical reactions varied with temperature. This equation indicates a rate constant that has a proportional relationship with temperature. For example, as the rate constant increases, the temperature of the chemical reaction generally also increases. The result is given below:

Where k is rate constant, Ea the activation energy, T the absolute temperature of the reaction and R is universal gas constant. A is called frequency factor or pre-exponential factor and proportional to the frequency of collisions between reacting molecules. A is independent of the absolute temperature T.

Equations (1), (2) and (3) are different forms of Arrhenius equation. A and Ea are called Arrhenius parameters.

Arrhenius Equation and Temperature Variation:

The relation between rate constant k and the absolute temperature T of the reaction is given by

For two different temperatures say T₁ and T₂ we have

Determination of Activation Energy:

We have

By knowing Values of K₁ and K₂ at temperatures T₁ and T₂ using experiments, the value of activation energy can be calculated.

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The occurrence of a bimolecular chemical reaction can be explained on the basis of collision theory.

The Collision of Reacting Molecules:

Consider a bimolecular general reaction

A  + B  →   C

In order for a chemical reaction to take place, the molecules of reactants A and B must collide. The rate of a chemical reaction depends on the rate of collision between the molecules. As the concentration and temperature increase, the rate of reaction also increases.

The Energy of Activation:

The collision between the molecules in a chemical reaction provides the kinetic energy needed to break the necessary bonds so that new bonds can be formed.  If the kinetic energy is not sufficient the bond between the reactants will not be broken and thus new bonds will not be formed. This required energy is called activation energy.

The activation energy (E_act) is defined as the minimum kinetic energy required for the molecular collision to lead to the reaction.

Thus reaction to take place the kinetic energy of colliding molecules should be greater than the activation energy.

The Orientation of Reacting Molecules:

The minimum kinetic energy (energy of activation) does not mean successful collision leading to the reaction.

For successful collision leading to the reaction, the colliding molecules must be so oriented relative to each other that the group reacting or bonds to be shifted are relatively close. This criterion is not essential for simple molecules but it becomes very much essential for complex molecules.

Potential Energy Barrier:

Consider a bimolecular general reaction

B  + AC   →   BA   +    C

During the collision the electron distribution about the three nuclei A, B and C changes in such a way that the new bond B-A strengthens at the same time the old bond A-C weakens. A stage is reached when all the three nuclei are weakly linked together. This state is called activated complex or transition state.

B   +   AC   →     B—-A —-C

The transition state is an unstable transitory complex of the highest energy state through which the reactants must pass on the way to products.  It decomposes spontaneously to form products.

To achieve this configuration, atoms require energy to overcome the repulsion between B and AC that have filled shells of electrons. This energy comes from kinetic energy due to the collision of reacting molecules and gets converted into potential energy in the activated complex. Thus transition state has the highest energy state. In an energy profile diagram (E.P.D.), the highest energy point (Peak) corresponds to the transition state.

Thus reactant molecules have to climb up the barrier to get converted into products.

Mathematical Treatment to Collision Theory:

Consider a bimolecular general reaction

B  + AC    →    BA   +    C

It is a second-order reaction. Hence the rate of collision is given by

Rate of collision = Z [AC] [B]

Where Z = frequency of collision.

The reaction rate is given by

Rate of reaction = P x f x Rate of collision

Where P is the fraction of collisions with proper orientations of colliding molecules. f is a fraction of molecules with sufficient kinetic energy.

Rate of reaction = P x f x Z [AC] [B]  …… (1)

Burt the rate of second-order reaction is given by

Rate of reaction = k [AC] [B] …… (2)

From (1) and (2) we have

k = P.f.Z

By Arrhenius equation we have

Where A = P.Z and called as frequency factor or pre-exponential factor.

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In this article, we shall study the molecularity of reaction and catalysis.

The Concept of Elementary Reactions:

Many reactions that follow a simple rate law are actually taking place in series of steps. These reactions are called complex reactions. Each step in a complex reaction is called elementary reaction. Thus complex reaction can be broken down into the elementary reactions.

An elementary reaction is defined as a reaction that takes place in a single step and can’t be broken down further into simplest chemical reactions.

Illustration:

Consider complex reaction

3 ClO^–_(aq)  →  ClO₃^–_(aq) + 2Cl^–_(aq)

Actually, this reaction takes place in two steps. Thus there are two elementary reactions.

Step-1:

2 ClO^–_(aq)  →  ClO₂^–_(aq) +  Cl^–_(aq)    (Bimolecular reaction)

Step – 2:

ClO₂^–_(aq)  +  ClO^–_(aq)  →  ClO₃^–_(aq) +  Cl^–_(aq)    (Bimolecular reaction)

The sum of the two reactions gives the overall reaction.

Molecularity of Elementary Reactions:

The molecularity of an elementary reaction is defined as the number of reaction molecules taking part in the reaction.

Example of Unimolecular Reaction:

O_3(g)  →  O_2(g) +  O_(g) 

C₂H₅I_(g)  →  C₂H_4(g) +  HI_(g) 

Example of Bimolecular Reaction:

O_3(g)  +  O_(g)  →  2O_2(g)

2NO_2(g)  → 2NO_(g)   +  O_2(g)

Distinguishing Between Molecularity and Order of Reaction:

Molecularity of a Reaction:

• The molecularity of a reaction is defined as the number of reaction molecules taking part in the reaction.
• Molecularity is always a whole number.
• It is a theoretical property indicating the number of molecules involved in each act leading to the reaction.
• It does not change with experimental conditions.
• It is the property of elementary reaction and has no meaning for a complex reaction.

Order of a Reaction:

• The overall order of the reaction is defined as the sum of the exponents to which the concentration terms in the rate law are raised.
• order of reaction may be an integer, fraction, or zero.
• It is a purely experimental property indicating the dependence of the observed reaction rate on the concentration of the reactants.
• It may change with experimental conditions.
• It is the property of both elementary and complex reactions.

Multistep Reactions:

A multistep reaction is a reaction involving two or more steps. Consider the reaction

A       →     C

It consists of two steps.

First step:         A    →    B

Second step:    B    →   C

In the above reaction, B is intermediate. The Intermediate is the product of the first step and reactant of the second step.

Reaction Intermediates:

The additional species other than the reactants or products formed in the mechanism during the progress of a reaction is called reaction intermediate.

Characteristics of Intermediate:

• They may be stable or unstable.
• The number of Intermediates in a reaction =  The number of Steps  –   1
• Thus reaction involving two steps will have one intermediate and one step reaction will have no intermediate.
• The intermediates appear in mechanism but do not appear in overall reaction because they are produced in one step and consumed in another step.
• The concentration of reaction intermediates is very small, hence cannot be determined easily.
• The rate of reaction is independent of the concentration of intermediates.
• The life period of reaction intermediates is very small hence they cannot be isolated.

Catalysis:

Catalyst and its Effect on the Rate of Reaction:

A catalyst is a substance, added to the reactants, that increases the rate of reaction without itself being consumed in the reaction

Example: In preparation of O₂ from KClO₃ in laboratories MnO₂ is used as a catalyst.

Characteristics of Catalyst:

• The catalyst does not appear in an overall reaction because they are consumed in one step and regenerated in another step.
• A catalyst lowers the activation energy of a reaction.
• In presence of a catalyst the height of the energy barrier decreases. Thus the number of molecules the possess the minimum kinetic energy increases.
• Chemically, the catalyst remains unchanged during a reaction.
• Catalyst does not change the quantity of the product.
• A catalyst is specific, which means different chemical reactions may have a different catalyst.
• Just a small amount needed to achieve a big increase in the rate of reaction.
• More amount of catalyst used can further increase the rate of reaction.
• A catalyst in powder form can further increase the rate of reaction.
• A catalyst may undergo a physical change in a reaction.

Distinguishing Between Catalyst and Reaction Intermediate:

Catalyst:

• A catalyst is a substance, added to the reactants, that increases the rate of the reaction without itself being consumed in the reaction.
• A catalyst increases the rate of a reaction.
• A catalyst is present at the start of the reaction.
• A catalyst is consumed in one step and regenerated in the subsequent step.
• The concentration of catalyst may appear in rate law.
• Catalysts are stable under ordinary conditions.

Intermediate:

• The additional species other than the reactants or products formed in the mechanism during the progress of a reaction is called reaction intermediate.
• Intermediate has no effect on the rate of reaction.
• An intermediate exist during the mechanism of the reaction.
• An intermediate is produced in one step and consumed in the subsequent step.
• The concentration of intermediate does not appear in rate law.
• Intermediates are highly unstable and ha a short life.

Note:

Both catalyst and intermediate do not appear in overall reaction.

Rate Determining Step (R.D.S.)

In a multistep reaction, rate of overall reaction depends upon the rate of the slowest step.  This slowest step is called rate determining step.

Example : Consider substitution reaction

R-X       +      Y        →      R-Y     +      X

Substrate   Reagent       Product    Living group

This reaction takes place as  follows

First Step:

R – X   →   R⁺  +     : X^–

Second Step:

R⁺  +   : Y^–  →   R  Y

In above case rate of overall reaction depends on the rate of the first step. Hence the first step is labelled as R.D.S.

The overall reaction cannot take place faster than the rate of rate determining step. Hence RDS step determines rate of overall reaction. As RDS is elementary reaction, the rate law can be determined from its stoichiometric equation. In rate law the exponents are equal to the coefficient of balanced equation for the step.

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In this article, we shall study the analytical treatment to the zero-order reaction, and the rate of zero-order reaction.

Order of Reaction:

The overall order of the reaction is defined as the sum of the exponents to which the concentration terms in the rate law are raised.

Let us consider a general reaction

aA  + bB  → Products

The rate law can be written as

Rate = K  [A]^x [B]^y …………… (1)

Thus the overall order of the reaction is (x + y).

Zero Order Reaction:

Integrated Law for Zero-Order Reaction:

A reaction whose rate is independent of the concentration of reactants is called a zero-order reaction.

Let us consider a general reaction

Let [A]_o be initial concentration of A (i.e at t = 0)  and be final concentration of A (i.e at t = t)

Integrating both sides of above equation

This relation is known as integrated law for zero-order reaction.

Expression for the Integrated Rate Constant:

From equation (1) we have

This is an expression of the integrated rate constant for the zero-order reaction.

Unit of Integrated Rate Constant:

The unit of  integrated rate constant is  mol dm^-3 t^-1 ( mol dm^-3 s^-1 or  mol dm^-3 min^-1,  mol dm^-3hr^-1)

Half-Life of Zero Order Reaction:

The half-life of a reaction is defined as the time required for the reactant concentration to fall to one half of its initial value. Thus for t = t_1/2,   [A]_t  = ½[A]_o

The  integrated rate constant for the zero-order reaction is given by

This is an expression of the half-life of a zero-order reaction.

Graphical Representation of Zero Order Reaction in Different Ways:

The graph of rate of reaction against time:     

The differential rate law for the zero-order reaction is

Thus the graph of the rate of reaction versus time is a straight line parallel to the time axis.

The graph of Rate of reaction against Initial Concentration:  

The differential rate law for the zero-order reaction is

Thus the rate is independent of the concentration of reactants. Hence Thus the graph of the rate of reaction versus concentration of reactants is a straight line parallel to concentration axis.

The graph of Concentration of the reactants against time:

The differential rate law for the zero order reaction is

[A]_t  = – kt + [A]_o

It is of the form y = mx + c. Thus the graph of concentration at instant versus time is a straight line with y-intercept. [A]_o. The slope of the straight line is – k.

Examples of Zero-order Reaction

• Decomposition of NH₃ on a hot platinum surface:

• Decomposition of Nitrous oxide in presence of platinum as a catalyst:

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In this article, we shall study the order of reaction and the analytical treatment to the first-order reaction, and the rate of the first-order reaction.

Order of Reaction:

The overall order of the reaction is defined as the sum of the exponents to which the concentration terms in the rate law are raised.

Let us consider a general reaction

aA  + bB  → Products

The rate law can be written as

Rate = K  [A]^x [B]^y …………… (1)

Thus the overall order of reaction is (x + y).

Example:

In the reaction, 

NO_2(g)   +   CO_(g)  →  NO_(g)   + CO_2(g)

The rate of reaction is experimentally found to proportional

to [NO₂]² and independent of [CO]. Thus x = 2 and y = 0

Thus the rate law of reaction is

Thus the overall order of the reaction is 2.

Characteristics of Order of Reaction:

• Order of reaction represents the number of atoms, ions and molecules whose concentration influence the rate of reaction.
• Order of the reaction is defined as the sum of the exponents to which the concentration terms in the rate law are raised. Thus it is not dependent on the stoichiometric coefficients in a balanced chemical reaction.
• Values of x and y are determined experimentally. The values of x and y in the rate law are not necessarily equal to the stoichiometric coefficients of reactants. Thus the order of reaction can be decided by performing experiment only.
• Order of reaction is defined in terms of concentration of reactants only and not of products.
• Order of reaction may be integer, fraction or zero.

Reactions with No Order:

If the rate of reaction cannot be expressed in the form, Rate, then the reaction has no order and term order should not be used for such reactions.

Example:

Clear Concept of Stoichiometric Coefficients of Balanced Chemical Equations and Exponents in Rate Law:

Let us consider a general reaction

aA  + bB  → Products

The stoichiometric coefficients of A and B are a and b.

Let us assume that the rate of reaction depends on [A]^x and [B]^y

The rate law is written as

Rate = K  [A]^x [B]^y …………… (1)

The values of x and y for the reaction are found experimentally. The values of x and y may be integer, fraction or zero.

First Order Reactions:

Integrated Rate Law For First Order Reaction:

The equations which are obtained by integrating the differential rate laws and which gives the direct relationship between the concentrations of the reactants and time is called integrated rate laws. A reaction whose rate depends on the single reactant concentration is called the first-order reaction.

Let us consider a general reaction

Let [A]_o be initial concentration of A (i.e at t = 0)  and [A]_t be the final concentration of A (i.e at t = t)

Integrating both sides of above equation

This relation is known as exponential integrated law for first order reaction.

The Expression for the Integrated Rate Constant for First Order Reaction:

This is an expression for the integrated rate constant for the first order reaction.

The expression for the integrated rate constant in terms of initial concentration for First Order Reaction:

Let a mol dm^-3 be the initial concentration of A (i.e at t = 0) and at some instant ‘t’ the decrease in concentration is x mol dm^-3.  (i.e at t = t). Thus   [A]_o = a and  [A] = a – x

Substituting in equation (2) we have

This is an expression for the integrated rate constant for the first order reaction in terms of initial concentration.

Unit of  the Integrated Rate Constant for the First Order Reaction:

The integrated rate constant for the first order reaction is given by

The quantity [A]_o / [A]  is a pure ratio. Hence it has no unit. Thus the unit of  integrated rate constant is per unit time (s^-1 or  min^-1 , hr^-1 )

Half-Life of First Order Reaction:

The half-life of a reaction is defined as the time required for the reactant concentration to fall to one half of its initial value. Thus for t = t1/2,  [A] = ½ [A]_o

The  integrated rate constant for the first order reaction is given by

This is an expression for the half-life of the first-order reaction.

Graphical Representation of Half-Life:

A graph is drawn by plotting time as a multiple of half-life on the x-axis and the concentration of reactant in terms of original concentration on the y-axis at that instant. The graph is as follows.

The graph shows that it is an exponential process. Thus this process will never complete. i.e. the graph will never touch x-axis.

Note: Such graph is shown by the disintegration of a radioactive element. The radioactive elements obey decay law.

Graphical Representation of the First Order Reaction in Different Ways:

The graph of Rate of reaction against time:     

The differential rate law for the first order reaction is

It is of the form y = mx + c. Thus the graph of rate reaction versus concentration at an instant  is a straight line passing through the origin (since c = 0). The slope of the straight line is k.

The graph of Concentration of the reactants of against time:

The exponential rate law for the first order reaction is [A]_t = [A]_o e^-kt

Thus it is an exponential process. Thus this process will never complete. i.e. the graph will never touch x-axis.

The graph of Concentration of the reactants against time:

This equation is of form y = mx + c. Thus the graph of  log₁₀[A]_t  versus time is a straight line with y-intercept log₁₀[A]₀.

The graph of log₁₀([A]₀/ [A]_t) against time:

This equation is of form y = mx + c. Where c = 0. Thus the graph of  log₁₀([A]₀/ [A]_t) versus time is  a straight line passing through the origin

Examples of First-order Reactions:

Pseudo First Order Reaction:

The reactions that have higher order true rate law are found to behave as the first order are called pseudo-first order reactions.

Examples of Pseudo First Order Reactions:

• Hydrolysis of methyl acetate:

CH₃COOCH_3(aq)  + H₂O_(l) → CH₃COOH_(aq)) + CH₃OH_(aq)

The true rate law of reaction must be

Rate = K'[CH₃COOCH₃][H₂O]

Thus it seems that the rate of reaction is dependent on two reactants.

But the concentration [H₂O]  is constant (say k’’)

Rate = K’ K”[CH₃COOCH₃]

Hence,  Rate = K[CH₃COOCH₃]

Thus the reaction actually a first order reaction. Hence it is called as pseudo first order reaction.

• Hydrolysis of cane sugar (sucrose):

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In this article, we shall discuss the concept of chemical kinetics, rate of reactions, and types of reactions on the basis of their rates.

Rate of Reaction:

The branch of chemistry, which deals with the rate of chemical reactions, the factors affecting the rate of reactions and the mechanism of the reaction. is called chemical kinetics.

Importance of Chemical Kinetics:

• It gives an idea that how fast a reaction can occur. using which we know how quickly a medicine is able to work or what is the time required for completion of the reaction.
• In environmental chemistry, it is important to study the ozone balance in the upper atmosphere. The maintenance and depletion of the ozone layer depend on the relative rate of formation and destruction of ozone in the upper atmosphere.
• It is important in catalysis. It is used to solve industrial problems such as the development of catalysts to synthesize new materials.
• It has biological importance. In our body, large protein molecules called enzymes, increase the rate of biological reactions.
• It is important in the food industry. It is used to determine the factors which spoil the food and the rate at which the food is getting spoilt. Hence the probable expiry date or best before the date can be determined.
• The fast setting ceramic material is used for the material for dental fillings.
• It is used to determine the rate at which steel rusts.
• It is used to study the rate at which fuel burns in an automobile engine.

Classification of Chemical Reactions on the Basis of the Rate of the Reaction:

Fast/Instantaneous Reactions (Type – I):

The chemical reaction which completes in less than 1ps (one pieco second) (10^-12 s) time, is known as the fast reaction. It is practically impossible to measure the speed of such reactions. The reason for a very fast rate of such reaction is that no chemical bonds are to be broken among the reactants.

e.g., ionic reactions. Organic substitution reactions, neutralization reaction.

Very Slow Reactions (Type – II):

Chemical reactions which complete in a long time from some minutes to some years are called slow reactions. The rates of such reactions are hardly of any physical importance.

e.g. rusting of iron, transformation of carbon into diamond etc.

Moderately Slow Reactions:

Chemical reactions which are intermediate between slow and fast reactions are called moderately slow reactions.

These reactions proceed at a moderate speed which can be measured easily. Mostly these reactions are in molecular nature.

Note:

The rate of chemical reaction can be changed by changing the conditions under which they occur.

Rate of a Reaction:

The rate of a chemical reaction may be defined as the change in concentration of designated species (reactant or product) per unit time. The rate can be measured qualitatively or quantitatively.

Qualitative Rate: The qualitative rate is based on certain visual parameters such as disappearance of reactants, colour change, effervescence etc.

Quantitative Rate: The quantitative rate is based on the rate of decrease in the concentration of any one reactant or the rate of increase in the concentration of any one product.

Average Rate of Reaction:

The average rate of reaction is defined as the change in concentration of reactant or product divided by the time interval over which the change occurs.

Consider a general reaction

Positive sign indicates that the concentration of B is increasing. It is to be noted that the rate of reaction is always positive.

The rate of reaction is expressed in terms of moles per litre per unit time (mol L^-1t^-1) or molar per unit time (Mt^-1). If time is measured in a second then the unit is moles per litre per second (mol L^-1s^-1) or molar per second (Ms^-1). In terms of partial pressure (for gaseous reactions) units is atmosphere per unit time. The average rate of reaction depends on the time interval chosen.

Average Rates of Some Reactions:

Example – 1:

In this case, stoichiometric coefficients of the reactants and products are same, the rate of the reaction is

Example – 2:

In this case, stoichiometric coefficients of H₂, N₂ and NH₃ are  1, 3 and 2 respectively. Hence the rate of the reaction is

Example – 3:

In this case, stoichiometric coefficients of N₂O₅, NO₂ and O₂ are  2, 4 and 1 respectively. Hence the rate of the reaction is

General Example:

aA  + bB  → cC   +   dD

In this case, stoichiometric coefficients of A, B, C and D are a, b, c and d respectively. Hence the rate of the reaction is

Instantaneous of Rate of a Reaction:

The rate of a reaction at a specific instant is called an instantaneous rate.

If the average rate of reaction is calculated for a shorter and shorter interval of time, a rate at a specific instant can be obtained. The instantaneous rate at the beginning of a reaction is called the initial rate of the reaction.

Consider a general reaction

Example – 1:

In this case, stoichiometric coefficients of H₂, N₂ and NH₃ are  1, 3 and 2 respectively. Hence the rate of the reaction is

General Example:

aA  + bB  → cC   +   dD

In this case, stoichiometric coefficients of A, B, C and D are a, b, c and d respectively. Hence the rate of the reaction is

Note:

In chemical kinetics, we deal only with the instantaneous rate of reaction only. Hence the instantaneous rate of reaction is referred as the rate of reaction only.

Graphical Representation of Instantaneous and Average Rate of Reaction in terms of Reactants:

Graphical Representation of Instantaneous and Average Rate of Reaction in terms of Products:

Determination of Rate of Reaction:

Determination of Average Rate of Reaction:

A graph is drawn by taking a concentration of species (reactant or product) on y-axis and time on the x-axis.

The average rate of reaction at time t can be obtained by the change in concentration (C₂ – C₁) of species (reactant or product) in the time interval t1 and t2. (t1 and t2 are equidistant from t) Then the average rate of reaction is calculated using following formula.

Determination of Instantaneous Rate of Reaction:

A graph is drawn by taking the concentration of species (reactant or product) on y-axis and time on the x-axis.

The instantaneous rate of reaction at time t can be obtained by drawing a tangent at time t and finding its slope at that point. The slope of the tangent to the curve at that point gives an instantaneous rate of reaction.

Reaction Life Time:

It is defined as the time taken by a reaction to proceed to 98% of completion. Shorter the life time, faster is the reaction. It is used to compare the rate of reactions.

Rate Laws and Rate Constant:

Law of Mass Action:

This law was given by Goldberg and Waage in 1864. It states that “at a given temperature, the rate of reaction at a particular instant is proportional to the product of the active masses of the reactants at that instant raised to powers which are numerically equal to the numbers of their respective molecules in the stoichiometric equation describing the reaction.”

Explanation:

Consider general reaction

aA  + bB  → cC  +  dD

By law of mass action

Rate ∝  [A]^a [B]^b

∴   Rate = K  [A]^a [B]^b

Rate Law:

The rate of chemical reaction is found to be proportional to the molar concentrations of the reactants raised to simple powers.

Let us consider a general reaction

aA  + bB  → Products

Let us assume the rate of reaction depends on[A]^x and [B]^y.

Thus, Rate ∝  [A]^x [B]^y

Rate = K  [A]^x [B]^y …………… (1)

But instantaneous rate of reaction is given by

This relation is known as the differential rate law or simply rate law. Where k is a constant called specific reaction rate constant or simply rate constant.

Definition:

The rate law is defined as an experimentally determined equation that expresses the rate of a chemical reaction in terms of molar concentrations of the reactants.

Rate Constant:

By rate law we have,  Rate = K  [A]^x [B]^y

If [A] = 1 and [B] = 1, Then

Rate = k = Rate Constant

The rate constant is defined as the rate of reaction would have if all the concentrations were set equal to unity.

Characteristics of Rate Constant:

• The values of the rate constant give an idea about the speed of the reaction. Greater the value of the rate constant, faster is the reaction.
• Each reaction has a definite value of the rate constant at a particular temperature.
• The value of the rate constant depends on temperature.
• The value of rate constant is independent of the concentration of reacting species.
• The value of rate constant depends on nature of reactant, the presence of catalyst, solvent and pH of a solution.
• The unit of rate constant depends on the order of the reaction. In general unit of rate constant is

Where n is the order of reaction.

Notes:

• The value of x and y in the rate law are not necessarily equal to the stoichiometric coefficients (a and b) of  A and B.
• Values of x and y are determined experimentally.

Example to Illustrate Rate Law:

Example:

In the reaction, NO_2(g)   +   CO_(g)  →  NO_(g)   + CO_2(g)

The rate of reaction is experimentally found to proportional

to [NO₂]² and independent of [CO]. Thus x = 2 and y = 0

Thus the rate law of reaction is

Applications of Rate Law:

• The rate law can be used to estimate the rate of a reaction for any given composition of the reaction mixture.
• It can be used to estimate the concentration of reactants and products at any time during the course of reaction.\
• The rate law is useful for prediction of the mechanism of a complex reaction.

Characteristics of Rate of Reaction:

• It is the speed at which the reactants are converted into products at any instant of time.
• It is dependent on the concentrations of the reactant species at that instant.
• As the reaction proceeds the rate of reaction decreases.

Characteristics of Rate Constant:

• It is constant of proportionality in rate law expression.
• It is independent of the concentration of reactants.
• It is constant throughout the reaction i.e. it is independent of the progress of the reaction.

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