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.

For More Topics in Thermal Properties of Matter and Thermodynamics Click Here

For More Topics in Physics Click Here

The post Thermodynamic or Temperature Scales appeared first on The Fact Factor.

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.

For More Topics in Thermal Properties of Matter and Thermodynamics Click Here

For More Topics in Physics Click Here

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

In this article, we should study the concept of phase, change of phase anfd the triple point of water.

Phase:

The phase of a substance is defined as its form which is homogeneous, physically distinct and mechanically separable from other forms of the substance. The term phase as used in thermodynamics refers to the fact that the matter exists either as a solid, liquid or gas. If we consider the example of water, it exists in the solid phase as ice, in the liquid phase as water and in the gaseous phase as vapour. All the substances can exist in any of the three phases under proper conditions of temperature and pressure.

Change of Phase:

The transitions from one phase to another takes place by the absorption or liberation of heat and usually by a change in volume and at a constant temperature. The temperature at which a phase change occurs also depends on pressure.

Phase Diagram:

The phase diagram is the graph drawn in which pressure is represented along y-axis and temperature is represented on the x-axis.

Phase diagram give the relationship between the phase in equilibrium in a system as a function of temperature, pressure and compositions. Phase diagrams are also known as Equilibrium diagrams or Constitutional diagrams.

A phase diagram indicates the temperature at which the solid will start and finish melting and the possible phase changes which will occur as a result of altering the composition or temperature.

The common point, where three lines of phases intersect is known as the triple point. At this point, the substance co-exists in equilibrium in all the three phases i.e. solid, liquid and vapour.

Characteristics of Phase Diagram:

• Different phases of a substance can be shown in a phase diagram.
• A region on a phase diagram represents a single phase of the substance, a curve represents an equilibrium between two phases and a common point represents an equilibrium between three phases.
• A phase diagram helps to determine the condition under which the different phases are in equilibrium.
• A phase diagram is useful for finding a convenient way in which desired change in phase can be produced

Phase Diagram for Water:

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

The region to the left of melting curve and above the sublimation curve represents the solid phase of water i.e. ice. The region to the right of melting curve and above the evaporation curve represents the liquid phase of water i.e. water. The region below 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 substance. Along any curve, the two phases can coexist in equilibrium.

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

Concept of Latent heat

The heat absorbed or released by a substance during the change of its physical state at constant temperature is called latent heat of the substance for that physical change.

Latent Heat of Fusion:

The quantity of heat required to convert unit mass of a solid into liquid state completely at its melting point and at constant temperature is called as latent heat of fusion.

Latent Heat of Vapourization:

The quantity of heat required to convert unit mass of a liquid into gaseous state completely at its boiling point and at constant temperature is called as latent heat of vapourization.

Concept of Internal and External Latent Heat:

Change of state of a substance is always accompanied by increase in the volume. Hence we can say that during the change of state there is always external work done. Thus the latent heat (L) supplied is used for two purposes.

The first part is used to do internal work i.e. to do the work against inter molecular force of attraction to increase the distance between the molecules. This part of latent heat is called internal latent heat. It is denoted by Li.

The second part is used to do external work i.e. to do the work against the external atmospheric pressure to increase the volume of the gas. This part of latent heat is called external latent heat. It is denoted by Le.

L = Li  + Le

But the external work done is given by

Le = P ∆V

Where P is a pressure and ∆V is change in the volume

Thus L = Li  +  P ∆V

This is the relation between internal latent heat and external latent heat.

Characteristics of Internal Latent Heat:

• The part of total latent heat which is used to do external work against intermolecular forces to increase the separation between the molecules is called internal latent heat.
• It increases the separation between molecules of the substances.
• It is greater than external latent heat.
• It is equal to the change in internal energy.

Characteristics of External Latent Heat:

• The part of total latent heat which is used to do external work against the external atmospheric pressure is called external latent heat.
• It increases the volume of the substances.
• It is less than external latent heat.
• It is equal to external work done.

Science > Physics > Themodynamics > Change of Phase

The post Change of Phase appeared first on The Fact Factor.

In this article, we shall study the concept of thermodynamics and thermodynamic state. Thermodynamics is a branch of physics that deals with the inter-conversion between heat energy and any other form of energy.

Thermodynamic State:

The simplest example of a system to which thermodynamics can be applied is a single chemically defined homogeneous substance. In this case, the thermodynamic state can be described completely by specifying any two of the three quantities, pressure P, volume V, and temperature T. These quantities are known as thermodynamic parameters or thermodynamic variables of the system.

For a given amount of the substance forming the system, these three quantities are not independent. They are connected by a relationship of the general form which is called equation of state. It is for this reason that any two of these quantities are sufficient to describe the thermodynamic state completely. The two quantities are then called the thermodynamic coordinates.

Terminology of Thermodynamics:

System:

The specified portion of the physical universe under thermodynamic study is called the system. e.g. A gas enclosed in a cylinder fitted with a piston is a system.

Surroundings:

Remaining part of the universe outside the system which can exchange energy with the system and which change the properties of the system is called a surrounding.

Universe:

The system and its surroundings are together known as the universe.

Boundary:

The real or imaginary surface separating the system from the surrounding is called the boundary

Isolated system:

A system which can exchange neither matter nor energy with the surroundings is called isolated system. Example:A liquid placed in a thermos flask is an isolated system. Temperature change outside the flask does not change the temperature of the liquid. (no energy transfer) and nothing can escape from or enter the flask (no transfer of matter). The total amount of energy remains constant. Both the mass and temperature of the system constant.

Homogeneous system:

When a system is a uniform throughout or consists of a single phase, it is said to be the homogeneous system. Example:A pure single solid, liquid or a gas. A mixture of gases.

Heterogeneous system:

A heterogeneous system is one which is not uniform throughout and which contains two or more phases which are separated from one another by definite boundary surface. Example:Two immiscible liquids such as benzene and water

Mechanical Equilibrium:

A thermodynamic system is said to be in mechanical equilibrium if no unbalanced forces and torques act between the system and the surroundings or between different parts of the system.

Thermal Equilibrium:

A thermodynamic system is said to be in thermal equilibrium if the temperature of the system is the same throughout and the temperature of the system and the surroundings is the same.

Chemical Equilibrium:

A thermodynamic system is said to be in chemical equilibrium if the chemical composition of the system is the same throughout.

Thermodynamic Equilibrium:

A thermodynamic system is said to be in thermodynamic equilibrium if it is in mechanical, thermal and chemical equilibrium at the same time.

Equation of a State:

The equation of state for any substance is a mathematical formula which expresses the relationship between the volume, pressure and temperature of the substance in any state of aggregation. Thus, for example, the equation of state for one mole a perfect gas is  PV = RT

The equation of the state can be written in the form, f(P, V, T) = 0.

The thermodynamic state of the system can be specified by stating the values of two coordinates. The value of the third variable can be determined by using the equation of state of the system.

Isothermal Process:

A process carried out at a constant temperature throughout the process is called isothermal process.

Isothermal Change:

When a  thermodynamic system  undergoes a  change in  its state at a constant temperature, the change is said to be Isothermal change. The condition of Isothermal change is given by dT = 0.

Conditions for Isothermal change:

The isothermal change can take place when the system is contained in a container having perfectly conducting walls due to which heat produced or absorbed during the change will flow out or flow in from the surrounding. Therefore, the temperature of the system remains constant.

In practice, no perfect container is available and therefore perfect occurrence of isothermal change is impossible. However, a fairly approximate isothermal change is obtained when the change is made slowly.

Examples of Isothermal Changes:

• Ice is converted into the water at constant temperature.
• Water is converted into vapours at constant temperature i.e. boiling point of water.

A gas can be allowed to expand or is compressed isothermally by changing the pressure on it.

Isothermals or Isotherm or Isothermal Curves:

A graph of pressure versus volume at constant temperature is called isotherm or isothermal or isothermal curve. D

A graph is drawn by taking pressure on the y-axis and volume on the x-axis. This graph is known as PV diagram or indicator diagram.

Consider a gas occupying a volume v1 at pressure P₁. The thermodynamic state of the gas is represented by a point H on the graph. Let us suppose that the gas undergoes an isothermal expansion from H to K along curve HK. Obviously, V₂ > V₁. During expansion, the gas does an external work and its internal energy decreases. The curve HK is known as Isothermal curve or Isothermal.

However, the change is made from K to H along curve KH, the gas undergoes an isothermal compression. Therefore, the volume of the gas decreases from V₂ to V₁. The external work is on the gas hence its internal energy increases.

For one mole of a perfect gas PV = RT  or  PV = constant. This relation at constant temperature is known as isothermal relation for a perfect gas.

Science > Physics > Themodynamics > Introduction

The post Introduction to Thermodynamics appeared first on The Fact Factor.

In this article, we shall study the laws of thermodynamics and the concept of work done in a process.

Zeroth Law of Thermodynamics:

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. This law introduces the concept of hotness and coldness which leads to the concept of the temperature of a body.

Characteristics of Thermal Equilibrium:

• When two bodies are kept in contact and there is no transfer of heat taking place between the two bodies, then the two bodies are said to be in thermal equilibrium with each other.
• When two bodies are in thermal equilibrium, there is no heat transfer between the two bodies due to conduction or convection.
• All bodies in thermal equilibrium are at equal temperatures.
• 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.

First Law of Thermodynamics:

Energy can’t be created nor destroyed but it can be converted from one form into the other (or forms) or into work. The total amount of energy of an isolated system remains constant, it may change from one form to another.

Mathematical Expression of First Law:

ΔQ  = ΔU +  ΔW

Where ΔQ  = Heat supplied to the system by the surroundings

ΔW = Work done by the system on the surroundings

Δ U = Change in internal energy of the system

Process and its Types:

Process:

It is the path or the operation by which a system changes from one state to another. A process causes a change in the value of at least one of the state functions.

Isothermal process:

If a process is carried out at a constant temperature, the process is called an isothermal process. e.g. Fusion of ice.

For an isothermal process, ΔT = 0, ΔU = 0. The internal energy (U) of a system remains constant during the isothermal process provided there is no change of phase.

Characteristics of Isothermal Process.

• In this process temperature of the system remains constant.
• The exchange of heat takes place with the surroundings.   ( ΔQ ≠ 0)
• Internal energy remains constant. ΔU = 0 (provided there is no change in a phase).
• The system is not thermally isolated from the surroundings.
• Expansion occurs with the absorption of heat, while compression occurs with the evolution of heat.
• ΔW  =  ΔQ
• In the case of gases, Boyle’s law is applicable i.e. PV = Constant

Adiabatic process:  

A process carried out in such a manner that the system, undergoing the change, does not exchange heat with the surroundings is called an adiabatic process. The temperature of the system changes during the adiabatic process. e.g. expansion of a gas in a vacuum.

Characteristics of Adiabatic Process.

• If a process is carried out in such a manner that the system, undergoing the change, does not exchange with the surroundings is called an adiabatic process.
• The exchange of heat with the surrounding does not take place.  ( q = 0)
• Internal energy varies. (ΔU ≠ 0)
• The system is thermally isolated from the surroundings.
• In expansion temperature and internal energy decreases, while in compression temperature and internal energy increase.
• W =  ΔU
• In the case of gases, PV^γ = Constant, where γ = Ratio of specific heat capacities of a gas

Second Law of Thermodynamics:

Mechanical work can be converted completely into heat but heat can not be completely converted into mechanical work, i.e. work and heat are not equivalent. Thus it is impossible to construct a 100 % efficient engine.

Heat Engines:

A heat engine is a device which takes heat from bodies at a higher temperature, converts part of it to mechanical work and remaining heat is rejected to the body at a lower temperature. The cycle is repeated again and again to get useful work.

Consider working of an internal combustion engine. In the cylinder of the engine, fuel is burned. The gases formed expand to move the piston. The arrangement converts reciprocating motion into rotational motion, which is responsible for the movement of an automobile. On the return stroke of the piston, the gases in the cylinder are expelled to the surroundings.

The efficiency of a heat engine is defined as the ratio of useful work (W) obtained from the heat engine to the heat input to the engine (Qi). Thus

Now work done W = Q_i – Q₂

Where  Q_i = Heat input

Q₂ = Heat rejected to surroundings

Refrigerators:

The refrigerator is a reverse of heat engines. It is a device which takes heat from bodies at a lower temperature, and heat is rejected to the surroundings at a higher temperature. Hence mechanical work is to be done.

In condenser of refrigerator working fluid (freon gas) is suddenly expanded due to which the mixture of vapour-liquid is formed. This mixture is compressed to a liquid. This liquid is then passed through or around the region to be cooled. This region is called the evaporator. In this region, the liquid is made to evaporate and the necessary heat for evaporation is removed from the region to be cooled. Thus heat is taken out from the body at a lower temperature. This liquid returns back in the condenser, where the heat is rejected to the surroundings which is at a higher temperature than the area to be cooled. Thus the cycle repeats. Mechanical work is to be done on the system, which is done by the compressor.

The coefficient of performance (COP) of a refrigerator is defined as the ratio of heat extracted from the cold reservoir to the work done on the system.

Thus COP  = Q₂ / W

Now work done W = Q_i – Q₂

Where Q_i = Heat input

Q₂ = Heat extracted from cold reservoir

Free Expansion:

When gas is made to expand when there is no external pressure, the expansion of a gas is called the free expansion of the gas. Free expansion of the gas is an irreversible process.

Quasi-Static Process:

The thermodynamic process which takes place infinitely slowly is called a quasi-static process. In practice, there is no process which is perfectly quasi-static. A quasi-static process is reversible and its direction can be reversed at any instant.

Example. Isothermal expansion of gas taking place very slowly in a cylinder fitted with a frictionless and weightless airtight movable piston.

Science > Physics > Themodynamics > Laws of Thermodynamics

The post Thermodynamics appeared first on The Fact Factor.

Chemical Thermodynamics and its Scope:

Energy stored in chemical substances is called chemical energy. Thermodynamics is the branch of science that deals with the different forms of energy, the quantitative relationships between them and the energy changes that occur in the physical and chemical process. Thermodynamics deals with all types of energies and conversion of one form of energy into other forms. Hence nowadays the term energetics is used in place of thermodynamics. Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics.

Limitations of Thermodynamics:

• Properties such as pressure, temperature, volume, and composition are the properties of matter in bulk. These properties are not based on the arrangement of atoms in molecules and molecular structures. Such properties are called macroscopic properties. Thermodynamics deals with macroscopic properties. It does not make use of any theory about atomic structure and molecular structure. Hence it is called macroscopic science.
• It helps to predict whether the chemical reaction can occur under a given set of conditions but it does not tell anything about the rate of reaction.
• It is more concerned with the initial and final states of the system. It does not tell anything about the mechanism of the process.
• It does not deal with the internal structure of molecules or atoms.

Terminology of Thermodynamics:

• System: The portion of the physical universe under thermodynamic study is called the system.
• Surroundings: The remaining part of the universe under thermodynamic study is called the surroundings.
• Boundary: The real or imaginary surface separating the system from the surrounding is called the boundary.

The boundary may be real or imaginary. It may be rigid or non-rigid. It may be conducting (diathermic) or non-conducting (adiabatic).

System + Surroundings = Universe

A given amount of one or more substances form the system. Thus, 100 kg of water placed in a flask constitutes the system. The air and flask in contact with water form the surroundings. A system is separated from the surroundings by real or imaginary boundary through which matter and energy can flow from the system to the surroundings and vice-versa.

Diagrammatic representation:

Types of Systems On the Basis of Exchange of Matter and Energy: 

Open System:

A system which can exchange both energy and matter with the surroundings is called an open system.

Example: A hot solution in a beaker is an open system because it can exchange both the matter  (vapours) and energy (heat) to the surroundings. All living organisms like plants and vegetables. (Total amount of energy does not remain constant. The mass and the temperature can undergo change).

Characteristics of  Open System:

• A system which can exchange both energy and matter with the surroundings is called an open system.
• The total amount of energy does not remain constant.
• The total amount of mass does not remain constant.

Closed system:

A system which can exchange energy but not matter with the surroundings is called a closed system.

Example: Water or gas in a closed (sealed) vessel. The substance can be heated or it can give out heat (energy exchange) but no substance can escape from the vessel. (Total amount of energy does not remain constant. Mass of the system remains constant but the temperature can undergo change)

Characteristics of Closed System:

• A system which can exchange energy but not matter with the surroundings is called a closed system.
• The total amount of energy does not remain constant.
• The total amount of mass remains constant.

Isolated system:

A system which can exchange neither matter nor energy with the surroundings is called an isolated system.

Example: A liquid placed in a thermos flask is an isolated system. Temperature change outside the flask does not change the temperature of the liquid. (no energy transfer) and nothing can escape from or enter the flask (no transfer of matter). (Total amount of energy remains constant. Both the mass and energy of the system constant).

Characteristics of  Isolated System:

• A system which can exchange neither energy nor matter with the surroundings is called isolated system.
• The total amount of energy remains constant.
• The total amount of mass remains constant e.g. hot solution kept in

Types of Systems On the Basis of Phases of Matter (composition):

Homogeneous system:

When a system is a uniform throughout or consists of a single-phase, it is said to be the homogeneous system.

Examples: A pure single solid, liquid or a gas. A mixture of gases. The true solution of a solid in the liquid.

Characteristics of Homogeneous System:

• When a system is a uniform throughout or consists of a single-phase, it is said to be the homogeneous system.
• This system contains only a single phase.
• This system is uniform throughout and hence there is no separation boundary between the constituents of the system

Heterogeneous system:

A heterogeneous system is one which is not uniform throughout and contains two or more phases which are separated from one another by definite boundary surface.

Examples: Mixture of two immiscible liquids such as benzene and water, The mixture of two or more solids.

Characteristics of Heterogeneous System:

• When a system is not uniform and contains three or more phases, it is said to be a heterogeneous system.
• This system contains two or more phases. The phases in this system are separated from one another by a definite boundary surface.
• The phases in this system are separated from one another by a definite boundary surface.

Universe as Isolated system:

The universe can be considered as an isolated system due to the following reasons

• The total mass and energy of the universe are conserved.
• The universe has no boundary, hence it has no surroundings.
• There is an interchange between different forms of energy due to natural and arranged processes within the universe.
• The natural or arranged process may be exothermic or endothermic due to which there is a change of temperature as it takes place in an isolated system.

Properties of System:

Extensive Properties:

A property that depends on the amount (or amounts) of the substance (or substances) present in the system is called extensive properties.

Examples: Volume, Mass and Energy are extensive properties.

Intensive Properties:

An intensive property of a system is one which is independent of the amount of the system and is a specific characteristic of the system.

Examples: Refractive index, density, surface tension.

State of a System:

To describe the system completely and ambiguously, macroscopic properties such as pressure, volume, temperature, mass (number of moles) and composition are used. By assigning numerical values to these properties, the state of a system can be defined.

State Function:

Any property of a system whose value depends on the current state of the system and is independent of the path followed to reach that state is called the state function.

Examples: Pressure (P), volume (V), Temperature (T) Internal energy (E) Enthalpy (H).

Characteristics of State Functions:

• If the values of some state function variables are changed, values of all other variables get adjusted automatically.
• When the state of the system is altered, the values of state functions change. the change in a state function (say x) ΔX, depends only on the state of a system before alteration (initial state) and that after alteration (final state) and is given by

Δ X  =  X_final  –  X_initial =   X₂  –  X₁

• ΔX is independent of the manner ( i.e. path) in which the state is altered
• ΔX is independent of the manner ( i.e. path) in which the state is altered

Significance of State Functions:

State functions are important thermodynamic property because it depends on initial and final states of the system but independent of the path followed by the system to bring about the change. The feasibility of a process can be verified using state functions because they are independent of the path followed by the system to bring about the change. For example, when ΔG is negative the process is spontaneous and can take place on its own when initiated. While when ΔG is positive the process is non-spontaneous and is to be arranged externally.

Path Function:

The property of the system whose value depends on the path used to reach a particular state is called a path function.

Examples: Work (W), Heat (q)

Thermodynamic Equilibrium:

A system is said to be in a state of thermodynamic equilibrium when the state functions of the system do not change with time. Thermodynamics deals with the system which is in states of thermodynamic equilibrium.  For such a state, the following three equilibria should exist simultaneously in the systems.

Thermal equilibrium: No change of temperature with time.

Chemical equilibrium: No change in chemical composition with time.

Mechanical equilibrium: No macroscopic movement i.e. no unbalanced force should act on or from within the system. Pressure remains constant though out in all parts of the system.

Different Types of Thermodynamic Equilibrium:

In chemical thermodynamics, for thermodynamic equilibrium, the system has to attain the following three types of equilibrium.

Thermal Equilibrium:

A system is said to be in thermal equilibrium with the surroundings when the system and surroundings are at the same temperature and there is no exchange of heat energy between them. In such an equilibrium total, the internal energy of the system remains constant.

Example: water in equilibrium with its vapours at a constant temperature.

Chemical Equilibrium:

A system is said to be in chemical equilibrium when the chemical composition of reactants and products do not change with time. Thus the chemical composition of a system as a whole remains constant. In such an equilibrium, the reaction does not stop it continues but the rate of the forward reaction is equal to the rate of backward reaction.

Example: N_2(g) +  3 H_2(g)   ⇌    2NH_3(g)

Mechanical Equilibrium:

A system is said to be in mechanical equilibrium when net force acting on the system is zero and the net moment of the system is zero. In such equilibrium, the system neither has translational motion nor has rotational motion.

Example: Column of a structure

Next Topic: Types of Chemical Processes

Science > Chemistry > Chemical Thermodynamics and Energetics > Introduction

The post Introduction to Chemical Thermodynamics appeared first on The Fact Factor.