Study Class 11 Physics Thermodynamics with clear notes on laws, processes, Carnot engine, and specific heat. Learn key concepts and formulas for better understanding.
Thermodynamics is the branch of physics that deals with heat, temperature and the inter-conversion of heat and other forms of energy. It is a macroscopic science that describes bulk systems using measurable variables like pressure, volume and temperature, without going into molecular details. In this chapter, you will learn how heat and work are two distinct modes of energy transfer that change the internal energy of a system. You will study the Zeroth Law, which introduces temperature, and the First Law, which is the law of conservation of energy applied to thermal systems. You will also explore specific heat capacities, thermodynamic processes such as isothermal, adiabatic, isochoric and isobaric, and the Second Law, which explains why some processes occur spontaneously while others do not. Finally, you will learn about the Carnot engine, reversible and irreversible processes, and the maximum efficiency of a heat engine.
What you'll learn
1Explain the concept of thermal equilibrium and the Zeroth Law of Thermodynamics.
2Distinguish between heat, internal energy and work as thermodynamic quantities.
3Apply the First Law of Thermodynamics to various processes.
4Define specific heat capacity and molar specific heat capacity, and use the relation Cp – Cv = R.
5Identify state variables and write the equation of state for an ideal gas.
6Describe quasi-static processes and analyse isothermal, adiabatic, isochoric and isobaric processes.
7State the Second Law of Thermodynamics and explain reversible and irreversible processes.
8Calculate the efficiency of a Carnot engine using η = 1 – T2/T1.
Chapter at a glance
01Thermal Equilibrium and Temperature
02Heat, Internal Energy, and Work
03First Law of Thermodynamics
04First Law of Thermodynamics
05Second Law of Thermodynamics
06Carnot Engine and Efficiency
07Thermodynamic Processes and State Variables
Detailed chapter notes
01
Thermal Equilibrium and the Zeroth Law
Two systems are in thermal equilibrium when their macroscopic variables do not change with time when they are in contact through a diathermic wall. The Zeroth Law states that if two systems A and B are separately in thermal equilibrium with a third system C, then A and B are in thermal equilibrium with each other. This law leads to the concept of temperature as the property that is equal for systems in thermal equilibrium. Temperature determines the direction of heat flow: heat flows from a hotter body to a colder body until both reach the same temperature.
Adiabatic walldoes not allow heat flow.
Diathermic wallallows heat flow.
Zeroth LawA and B in equilibrium with C implies A and B in equilibrium with each other.
02
Heat, Internal Energy and Work
Internal energy U is the sum of kinetic and potential energies of the molecules of a system, excluding the kinetic energy of the system as a whole. It is a state variable, depending only on the state of the system, not on how that state was reached. Heat and work are not state variables; they are modes of energy transfer. Heat is energy transfer due to a temperature difference, while work is energy transfer by other means, such as moving a piston. The internal energy of an ideal gas depends only on its temperature.
Internal energy U is a state variable.
Heat and work are path-dependent quantities.
For an ideal gas, U depends only on T.
03
First Law of Thermodynamics
The First Law of Thermodynamics is the principle of conservation of energy applied to systems where heat and work are involved. It states that the heat supplied to a system (ΔQ) is used partly to increase its internal energy (ΔU) and partly to do work (ΔW) by the system on the surroundings: ΔQ = ΔU + ΔW. For a gas expanding against a constant pressure P, the work done is ΔW = PΔV. The First Law shows that ΔQ – ΔW is path-independent and equals ΔU, which depends only on the initial and final states.
ΔQ = ΔU + ΔW
Work done by gas at constant pressureW = PΔV
For a cyclic process, ΔU = 0, so Q = W.
04
Specific Heat Capacity
The heat capacity S of a substance is the heat required to raise its temperature by 1 K: S = ΔQ/ΔT. Specific heat capacity s is heat capacity per unit mass: s = (1/m)(ΔQ/ΔT). Molar specific heat capacity C is heat capacity per mole: C = (1/μ)(ΔQ/ΔT). For solids, the law of equipartition gives C = 3R, which agrees with experiment at ordinary temperatures. For an ideal gas, two molar specific heats are defined: at constant pressure (Cp) and at constant volume (Cv), related by Cp – Cv = R. The specific heat of water is 4186 J kg⁻¹ K⁻¹.
s = (1/m)(ΔQ/ΔT), unit J kg⁻¹ K⁻¹
C = (1/μ)(ΔQ/ΔT), unit J mol⁻¹ K⁻¹
Cp – Cv = R for an ideal gas
05
Thermodynamic State Variables and Equation of State
An equilibrium state of a thermodynamic system is described by state variables such as pressure, volume, temperature, and mass. State variables are of two types: extensive variables (like volume, internal energy, mass) that depend on the size of the system, and intensive variables (like pressure, temperature, density) that do not. The equation of state relates these variables. For an ideal gas, the equation of state is PV = μRT. A P-V curve at constant temperature is called an isotherm.
Extensive variablesU, V, m
Intensive variablesP, T, ρ
Ideal gas equationPV = μRT
06
Thermodynamic Processes
A quasi-static process is infinitely slow, so the system remains in equilibrium with its surroundings at every stage. In an isothermal process, temperature is constant; for an ideal gas, PV = constant, and the work done is W = μRT ln(V2/V1). In an adiabatic process, no heat is exchanged; for an ideal gas, PV^γ = constant, where γ = Cp/Cv, and work done is W = μR(T1 – T2)/(γ – 1). In an isochoric process, volume is constant, so no work is done and ΔQ = ΔU. In an isobaric process, pressure is constant, and work done is W = PΔV = μR(T2 – T1). In a cyclic process, the system returns to its initial state, so ΔU = 0 and Q = W.
IsothermalT constant, PV = constant, W = μRT ln(V2/V1)
The Second Law of Thermodynamics disallows certain processes that satisfy the First Law. It has two equivalent statements: the Kelvin-Planck statement states that no process is possible whose sole result is the absorption of heat from a reservoir and its complete conversion into work. The Clausius statement states that no process is possible whose sole result is the transfer of heat from a colder object to a hotter object. These statements imply that no heat engine can have efficiency equal to 1, and no refrigerator can have an infinite coefficient of performance.
Kelvin-Planckno perfect heat engine.
Clausiusno perfect refrigerator.
The two statements are equivalent.
08
Reversible and Irreversible Processes
A reversible process is an idealised process that can be reversed so that both the system and the surroundings return to their original states with no other changes. It must be quasi-static and non-dissipative. In reality, all spontaneous processes are irreversible due to non-equilibrium states, friction, viscosity, and other dissipative effects. Examples of irreversible processes include free expansion of a gas, heat transfer due to finite temperature difference, and diffusion of gases. Reversibility is a limiting concept used to define the maximum efficiency of engines.
Reversiblequasi-static and no dissipative effects.
Irreversiblemost natural processes.
Examplesfree expansion, diffusion, heat flow due to temperature difference.
09
Carnot Engine and Efficiency
A Carnot engine is a reversible heat engine operating between two temperatures T1 (source) and T2 (sink). The Carnot cycle consists of two isothermal processes (expansion at T1 and compression at T2) connected by two adiabatic processes. The efficiency of a Carnot engine is η = 1 – T2/T1. No engine operating between the same two temperatures can have an efficiency greater than that of a Carnot engine. The efficiency is independent of the working substance. The relation Q1/Q2 = T1/T2 holds for a Carnot cycle, which can be used to define a universal thermodynamic temperature scale.
Two objects are said to be in thermal equilibrium when:
AThey have the same temperature and no heat flows between them
BThey are in contact with each other
CThey have the same mass
DThey are made of the same material
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Answer: (A) They have the same temperature and no heat flows between them
Thermal equilibrium is defined as a state where two bodies at the same temperature exchange no net heat. When temperatures are equal, the net heat flow is zero.
Question 02
Which of the following is the SI unit of heat?
ACalorie
BJoule
CErg
DNewton
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Answer: (B) Joule
The SI unit of heat energy is Joule (J). One calorie = 4.18 J.
Question 03
The first law of thermodynamics is a statement of which fundamental principle?
AConservation of energy
BConservation of momentum
CConservation of mass
DConservation of angular momentum
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Answer: (A) Conservation of energy
The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another, which is a direct application of the law of conservation of energy.
Question 04
Which of the following statements best defines the Second Law of Thermodynamics?
AEnergy can neither be created nor destroyed, only transformed
BThe entropy of an isolated system always increases or remains constant in any spontaneous process
CHeat always flows from a cold body to a hot body
DThe internal energy of a system depends only on its temperature
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Answer: (B) The entropy of an isolated system always increases or remains constant in any spontaneous process
The Second Law of Thermodynamics states that entropy of an isolated system increases for any spontaneous process. This is the fundamental statement distinguishing forward and reverse processes.
Question 05
The Carnot engine operates between two thermal reservoirs at temperatures T₁ (hot) and T₂ (cold). What is the maximum theoretical efficiency of a Carnot engine?
Aη = 1 - T₂/T₁
Bη = T₂/T₁
Cη = 1 - T₁/T₂
Dη = (T₁ - T₂)/(T₁ + T₂)
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Answer: (A) η = 1 - T₂/T₁
The Carnot efficiency formula is η = 1 - T₂/T₁, where temperatures must be in absolute scale (Kelvin). This represents the maximum possible efficiency for any heat engine operating between two temperatures.
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Q1. Define thermal equilibrium. How does the Zeroth Law of Thermodynamics lead to the concept of temperature?
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Model answer
Two systems are said to be in thermal equilibrium if they are separated by a diathermic wall and no net flow of heat occurs between them; their macroscopic variables do not change with time. The Zeroth Law states that if systems A and B are separately in thermal equilibrium with a third system C, then A and B are also in thermal equilibrium with each other. This implies a common property, called temperature, which is equal for all systems in thermal equilibrium.
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Q2. Distinguish between heat and internal energy. Why is internal energy considered a state variable while heat is not?
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Model answer
Internal energy is the sum of kinetic and potential energies of molecules in a system and depends only on the state of the system, not on how it was achieved. Heat is energy in transit due to temperature difference; it is not a property of the system. Internal energy is a state variable because its value depends only on the state, whereas heat depends on the path taken.
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Q3. State the first law of thermodynamics and write its mathematical expression. Explain the meaning of each term.
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Model answer
The first law of thermodynamics states that energy can neither be created nor destroyed; it can only be converted from one form to another. For a thermodynamic system, the heat supplied (ΔQ) equals the change in internal energy (ΔU) plus the work done by the system (ΔW). Mathematically, ΔQ = ΔU + ΔW. Here, ΔQ is heat supplied to the system, ΔU is change in internal energy, and ΔW is work done by the system on surroundings.
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Q4. State the Kelvin-Planck statement of the Second Law of Thermodynamics.
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No process is possible whose sole result is the absorption of heat from a reservoir and the complete conversion of the heat into work.
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Q5. State the four steps of a Carnot cycle in order.
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The four steps of a Carnot cycle are: (1) Isothermal expansion of the gas at temperature T1, absorbing heat Q1 from the hot reservoir. (2) Adiabatic expansion of the gas, causing its temperature to drop to T2. (3) Isothermal compression of the gas at temperature T2, releasing heat Q2 to the cold reservoir. (4) Adiabatic compression of the gas, raising its temperature back to T1.
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The Zeroth Law states that if two systems A and B are separately in thermal equilibrium with a third system C, then A and B are in thermal equilibrium with each other. This law leads to the concept of temperature as the property that determines thermal equilibrium.
What is the difference between heat and internal energy?
Internal energy is the sum of kinetic and potential energies of the molecules of a system, and it is a state variable. Heat is energy in transit due to a temperature difference between the system and its surroundings. Heat is not a state variable; it depends on the path taken.
State the First Law of Thermodynamics.
The First Law states that the heat supplied to a system (ΔQ) is used to increase its internal energy (ΔU) and to do work (ΔW) by the system: ΔQ = ΔU + ΔW. It is the law of conservation of energy applied to thermal systems.
What is the relation between Cp and Cv for an ideal gas?
For an ideal gas, the molar specific heat at constant pressure (Cp) and at constant volume (Cv) are related by Cp – Cv = R, where R is the universal gas constant.
What is a Carnot engine and what is its efficiency?
A Carnot engine is a reversible heat engine operating between two temperatures T1 (source) and T2 (sink). Its efficiency is given by η = 1 – T2/T1. No engine operating between the same two temperatures can have a higher efficiency.
Why are most natural processes irreversible?
Most natural processes are irreversible because they involve non-equilibrium states, friction, viscosity, or other dissipative effects. These factors prevent the system and surroundings from returning to their original states without external changes.