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 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.

In this article, we shall study the first law of thermodynamics and its application to different chemical processes.

Zeroth Law of Thermodynamics:

Statement:

If two bodies (say A and B) are in thermal equilibrium of the third body (say C) then body A and B will also be in thermal equilibrium with each other

Significance of the Law:

The common use of the thermometer in comparing the temperature of any two or more systems is based on the zeroth law of thermodynamics.

First Law of Thermodynamics:

Statement:

Different forms of the first law of thermodynamics are as follows

• Energy can’t be created nor destroyed but it can be converted from one form into the other (or forms) or into work.
• When a quantity of energy of one kind disappears, then an equivalent amount of energy of another kind makes its appearance.
• It is impossible to make a perpetual motion machine which would produce work without consuming energy.
• The total amount of energy of an isolated system remains constant, it may change from one form to another.
• The energy of the universe remains constant.
• For a system in contact with the surroundings, the sum of energies of the system and its surroundings remains constant however differently it may be shared between the two.

Mathematical Statement of the First Law:

Consider the system in state I (initial state) with internal energy U₁. It is converted into state II (final state) with internal energy U₂ by supplying ‘q’ amount of heat to it. During this process, some work “W” is done by the system on the surroundings. Heat absorbed by the system is used for a) increasing internal energy of a system and b) to do some mechanical work “W”. 

Now, Change in the internal energy of the system is equal to the heat supplied plus Work done.

Thus, Final internal energy = U₂ = U₁ +   q +

∴   (U₂ – U₁)   =      q + W

∴   ΔU = q   + W

In the pressure-volume type of work W = PΔV

∴   ΔU = q +  PΔV

This is the mathematical equation of the first law of thermodynamics.

Sign Conventions for q, W, and ΔU:

• When heat is absorbed by the system q is positive.
• When heat is rejected or given out by the system q is negative.
• When the work is done on the system by surroundings (Work of compression) then W is positive.
• When the work is done by the system on the surroundings (Work of expansion) then, W is negative.
• When there is an increase in the internal energy of the system (increase in temperature) ΔU is positive.
• When there is a decrease in the internal energy of the system (decrease in temperature) ΔU is negative.

Application of First Law of Thermodynamics to Different Chemical Processes:

Isothermal Process:

Internal energy is a function of temperature. As the temperature is constant, the internal energy is also constant. Hence there is no change in internal energy.     ΔU = 0

By the first law of thermodynamics,

ΔU = q   + W

∴ 0 = q   + W

∴ q = -W or W = – q

Thus in the isothermal process heat absorbed is entirely used for doing work on the surroundings or the work done by the surrounding at constant pressure results in the release of the heat (energy) by the system.

Adiabatic Process:

In an adiabatic process, there is no exchange of heat      q = 0

By the first law of thermodynamics

ΔU = q   + W

ΔU = 0   + W

∴   W = q

Thus the increase in internal energy of a system is due to work done by the surroundings on the system or work done by the system on the surroundings is due to the expense of internal energy of the system.

Isochoric Process:

In isochoric process there is no change in volume   ΔV = 0, Thus the work done W = P Δ V = 0

By the first law of thermodynamics,

ΔU = q   + W

∴ ΔU = q   + 0

∴ ΔU = q

Thus the increase in internal energy of a system is due to the absorption of the heat from the surroundings or the decrease in internal energy of a system is due to the release of the heat from the system to the surroundings.

Isobaric Process:

In isobaric process, there is no change in pressure   ΔP = 0 Thus work done W = – P_ext ΔV

By the first law of thermodynamics,

ΔU = q   + W

∴ ΔU = q   – P_ext ΔV

Thus the increase in internal energy of a system is due to the absorption of the heat from the surroundings or the decrease in internal energy of a system is due to release of the heat from the system to the surroundings.

Note:

Most of the chemical reactions take place at constant pressure.

Second Law of Thermodynamics:

We observe that heat flows from the hot end of a metal rod flows to its cold end. The opposite flow of heat is not taking place. The first law (law of conservation of energy) allows heat flow from cold end to hot end. It is possible when heat lost by the cold end is equal to the heat gained by hot end. Thus energy is conserved. But such heat transfer is not possible. Thus the first law of thermodynamics is insufficient to put a restriction on the direction of the heat flow.  To overcome the deficiency of the first law, the second law of thermodynamics is proposed using human experience.

Statement:

Heat cannot be completely converted into an equivalent amount of work without producing permanent changes either in the system or its surroundings. or The spontaneous flow of heat is always unidirectional, from higher temperature to lower temperature.

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