Introduction
The foundation of thermodynamics is the conservation of energy and the fact that heat flows spontaneously from hot to cold body and not the other way around. The study of heat and its transformation to mechanical energy is called thermodynamics. It comes from a Greek word meaning “Movement of Heat”.
In this chapter, we shall study the laws of thermodynamics, various thermodynamic processes, basic theory of heat engines, refrigerators and Carnot engine.
Thermal Equilibrium
When the temperature of the mixture becomes almost stable with the surrounding there is no further exchange of energy. This state in thermodynamics is called thermal equilibrium. So we may say in thermal equilibrium, the temperatures of the two systems are equal.
Zeroth Law of Thermodynamics
Zeroth law of thermodynamics states that “If two systems are in thermal equilibrium with a third system separately are in thermal equilibrium with each other.” Physical quantity whose value is equal for two systems in thermal equilibrium is called temperature (T).
Heat and Internal Energy
(i). Heat
Heat is that form of energy which gets transferred between a system and its surrounding because of temperature difference between them. Heat flows from the body at a higher temperature to the body at lower temperature. The flow stops when the temperature equalises. i.e., the two bodies are then in thermal equilibrium.
(ii). Internal Energy
It is sum of the kinetic energies and potential energies of all the constituent molecules of the system. It is denoted by ‘U’. U depends only on the state of the system. It is a state variable which is independent of the path taken to arrive at that state.
Recommended Books
- NCERT Textbook For Class 11 Physics Part 1 & 2
- CBSE All In One Physics Class 11 2022-23 Edition
- Oswaal CBSE Chapterwise Question Bank Class 11 Physics Book
- Modern's abc Plus of Physics for Class-11 (Part I & II)
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Work Done by a Gas
A container of cross sectional area A is fitted with a movable piston. Let the pressure of gas is P. Due to force applied by gas on piston, piston is displaced by Δx
Work done by gas,
`W=F.\triangle r`
`W=F \triangle x cos0`
`W=F \triangle x`
`W=PA \triangle x`
`W=P \triangle V`
First Law of Thermodynamics
The first law of thermodynamics is a particular form of the general law of conservation of energy. Suppose the amount of heat Q is supplied to a system. It is normally spent in two ways.
Partially, it is spent in increasing internal energy of system.
The remaining part of it is spent in expanding the body against the external pressure, i.e. in doing external work W.
If ΔU the change in internal energy "since energy can neither be created nor destroyed but only convert from one form to another", we have then
Q = ΔU + W............(1)
If dQ, dU and dW are infinitesimal changes in heat, internal energy and work respectively, then equation (1) becomes
dQ = dU + dW
This equation represents the differential form of first law of thermodynamics.
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Limitations of First Law of Thermodynamics
The first law of thermodynamics plays an important role in thermodynamics as it can be applied to know how much work will be obtained by transferring a certain amount of heat energy in a given thermodynamic process. However, first law of thermodynamics suffers from the following limitations :
- First law of thermodynamics does not indicate the direction of heat transfer.
- First law of thermodynamics does not tell anything about the conditions under which heat can be transformed into work.
- The first law does not indicate as to why the whole of the heat energy cannot be continuously converted into mechanical work.
Specific Heat Capacity
Specific heat capacity of a substance is defined as the heat required to raise the temperature of unit mass through 1°C (or 1 K).
Heat capacity of a substance is given by
`S=\frac{\triangle Q}{\triangle T}`
If we divide S by mass of the substance m in kg, we get
`C=\frac{S}{m}=\frac{1}{m}\frac{\triangle Q}{\triangle T}`
here s is known as the specific heat capacity of the substance. It depends on the nature of the substance and its temperature. The unit of s is J kg–1 K–1.
The specific heat at constant volume Cv
It is defined as the amount of heat required to raise the temperature of a 1 mole of a gas through 1°C when its volume is kept constant. It is denoted by (Cv) and given by
`C_V=\left(\frac{\triangle Q}{\triangle T}\right)_V`
The specific heat at constant pressure Cp
It is defined as the amount of heat required to raise the temperature of 1 mole of the gas through 1°C when its pressure is kept constant. It is denoted by (Cp) and given by
`C_P=\left(\frac{\triangle Q}{\triangle T}\right)_P`
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Derivation of Mayer's Formula
From 1st law,
ΔQ = ΔU + ΔW = ΔU + PΔV
At constant volume ΔV = 0 so ΔQ = ΔU
`C_{v}=(\frac{ΔQ}{ΔT})_{v}=(\frac{ΔU}{ΔT})_{v}`
`C_{v}=\frac{ΔU}{ΔT}`
On the other hand, at constant pressure,
ΔQ = ΔU + PΔV
`C_{p}=(\frac{ΔQ}{ΔT})_{p}=(\frac{ΔU}{ΔT})_{p}+P(\frac{ΔV}{ΔT})_{p}`
Now, for a mole of an ideal gas
PV = RT
`\frac{ΔV}{ΔT}=\frac{R}{P}`
`C_{p}=(\frac{ΔU}{ΔT})_{p}+\frac{P\times R}{P}`
`C_{p}=C_{v}+R`
`C_{p}-C_{v}=R`
This formula is known as Mayer's Formula. All the three quantities (Cp), (Cv) and R in this equation should be expressed in the same units either in joule/mole°C or in cal/mole°C.
Thermodynamic state variables and equation of state
The parameters or variables which describe equilibrium states of the system are called state variables.
(i). Intensive Variable
These are the variables which are independent of the size. e.g., pressure, density and temperature.
(ii). Extensive Variable
These are the variables which depend on the size of the system. e.g., volume, mass, internal energy.
(iii). Equation of State
The relation between the state variables is called the equation of state.
Thermodynamic processes
Any change in the thermodynamic coordinates of a system is called a process. The following are familiar processes in the thermodynamics.
(i). Isothermal Process
When a thermodynamic system undergoes a process under the condition that its temperature remains constant, then the process is said to be isothermal process. The essential condition for an isothermal process is that the system must be contained in a perfectly conducting chamber.
For isothermal process,
ΔU = 0
from the first law of thermodynamics,
ΔU = Q-W
0 = Q-W
Q = W
Hence, for an ideal gas all heat is converted into work in isothermal process.
(ii). Adiabatic Process
When a thermodynamic system undergoes a process under the condition that no heat comes into or goes out of the system, then the process is said to be adiabatic process. Such a process can occur when a system is perfectly insulated from the surroundings.
For adiabatic process,
Q = 0
from the first law of thermodynamics,
ΔU = Q-W
ΔU = 0-W
ΔU = -W
(iii). Isobaric Process
If the working substance is taken in expanding chamber in which the pressure is kept constant, the process is called isobaric process. In this process the gas either expands or shrinks to maintain a constant pressure and hence a net amount of work is done by the system or on the system.
(iv). Isochoric Process
If a substance undergoes a process in which the volume remains unchanged, the process is called an isochoric process. The increase of pressure and temperature produced by the heat supplied to a working substance contained in a non-expanding chamber is an example of isochoric process.
For isochoric process,
ΔV = 0, W = PΔV, W = 0
from the first law of thermodynamics,
ΔU = Q-W
ΔU = Q-0
ΔU = Q
(v). Quasi Static Process
A quasi-static process is defined as the process in which the deviation from thermodynamics equilibrium is infinitesimal and all the states through which the system passes during quasi-static process may be treated as aquarium states. Thus it may be defined as a succession of equilibrium states.
Heat engines
Any "cyclic" device by which heat is converted into mechanical work is called a heat engine. For a heat engine there are three essential requirements :
Source:- A hot body, at a fixed high temperature T1 from which the heat can be drawn heat, is called source or hot reservoir.
Sink:- A cold body at a fixed lower temperature T2 to which any amount of heat can be rejected, is called sink or cold reservoir.
Working Substance:- The material, which on being supplied with heat, performs mechanical work is called the working substance.
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| Heat Engine |
In a heat engine, the working substance takes in heat from the source, converts a part of it into external work, gives out the rest to the sink and returns to its initial state. This series of operations constitute a cycle. The work can be continuously obtained by performing the same cycle over and over again.
Suppose the working substance takes in an amount of heat Q1 from the source, and gives out an amount Q2 to the sink. Let W be the amount of work obtained. The net amount of heat absorbed by the substance is Q1 - Q2, which has been actually converted into work. Applying the first law of thermodynamics to one complete cycle. We get
Q1 - Q2 = W
Thermal Efficiency
The thermal efficiency (e) of an engine is defined as the ratio of the work obtained to the heat taken in from the source, that is,
`\e=\frac W{Q_1}=\frac{Q_1-Q_2}{Q_1}`
`\e=1-\frac{Q_2}{Q_1}`
This equation indicates that the efficiency of the heat engine will be unity (efficiency 100%) when Q2 = 0. This is, however, not possible in practice, This means that the engine cannot convert all the heat taken in from the source into work.
Refrigerators and heat pumps
(i). Reversible Process
A reversible process is one which can be retraced in opposite order by slightly changing the external conditions. The working substance in the reverse process passes through all the stages as in the direct process in such a way that all changes occurring in the direct process are exactly repeated in the opposite order and inverse sense and no changes are left in any of the bodies participating in the process or in the surroundings.
For reversible process,
ΔU = 0
from the first law of thermodynamics,
ΔU = Q-W
0 = Q-W
Q = W
(ii). Irreversible Process
Those process which can not be retraced in the opposite order by reversing the controlling factors are known as irreversible processes.
Second law of thermodynamics
This has two statements. First is Kelvin-Planck statement which is based upon the performance of heat engine and second is Clausius statement which is based upon the performance of refrigerator.
Kelvin-Planck statement
This may be stated as, "It is impossible to construct a device which operating in a cycle, has a sole effect of extracting heat from a reservoir at performing an equivalent amount of work". Thus, a single reservoir at a single temperature can not continuously transfer heat into work.
Clausius statement
This may be stated as, "It is impossible for a self-acting machines working in a cycle process, unaided by any external agency to transfer heat from a body at a lower temperature to a body at a higher temperature." In other words it may be stated as "Heat cannot flow itself from a colder to a hotter body".
Reversible and Irreversible Processes
Reversible Process: A thermodynamic process is said to be reversible if the process can be turned back such that both the system and the surroundings return to their original states, with no other change anywhere else in the universe. Ex- extension of springs, slow adiabatic compression or expansion of gases.
Irreversible Process: An irreversible process can be defined as a process in which the system and the surroundings do not return to their original condition once the process is initiated. Ex- Relative motion with friction, Heat transfer.
Carnot Engine
A reversible heat engine operating between two temperatures is called a Carnot engine and the sequences of steps constituting one cycle is called the Carnot cycle.
Carnot Theorem
Carnot gave the most important results which are:
No engine can have efficiency more than that of the Carnot engine.
The efficiency of the Carnot engine is independent of the nature of the working substance.
Summary
Thermodynamics : It is study of exchange of heat energy among bodies and conversion of heat energy into machenical energy and vice-versa.
Thermal Equilibrium : Two or more systems are said to be in thermal equilibrium, if there is no exchange of heat energy between them when they are brought in thermal contact.
Internal Energy : It is sum of the kinetic energy of all constituent particles of the system and the potential energy of interaction among these particles.
Isothermal Process : The process during which the temperature of the system remains constant.
Adiabatic Process : The process during which heat is neither given to the system, nor taken from it.
Isochoric Process : The process during which the volume remains constant.
Isobaric Process : The process during which the pressure remains constant.
Quasi-static Process : The process in which the system departs only infinitesimally from the equilibrium state.
Cyclic Process : The process in which the system returns to its initial state.
Reversible Process : The process in which the system can be retraced to its original state by reversing the conditions.
Irreversible Process : The process in which the system cannot be retraced to its original state by reversing the conditions.
Heat Engine : It is a device by which a system is made to undergo a cyclic process that results in conversion of heat into work.
Zeroth law of thermodynamics states that ‘two systems in thermal equilibrium with a third systems are in thermal equilibrium with each other’.
The internal energy of an ioslated system is constant.
Second law of thermodynamics does not allow some processes which are consistent with the first law of thermodynamics. It states
Clausius statement : No process is possible whose sole result is the transfer of heat from a colder object to a hotter object.
Kelvin-Planck statement : No process is possible whose sole result is the absorption of heat from a reservoir and complete conversion of the heat into work.
