Thermodynamics and Kinetic Theory JEE Notes: Download Now

Thermodynamics studies heat, work, temperature and energy transfer at a macroscopic level, while kinetic theory explains the same behaviour by analysing the motion of molecules. Together, they connect pressure, temperature and volume with molecular motion. These Thermodynamics and Kinetic Theory JEE Notes cover the zeroth and first laws, thermodynamic processes, PV diagrams, Carnot engines, entropy, kinetic theory, molecular speeds, degrees of freedom and specific heats for quick JEE revision.

Thermodynamics and Kinetic Theory JEE Notes: Heat, Work and Internal Energy

Thermal Equilibrium and Zeroth Law

Two bodies are said to be in thermal equilibrium when they have the same temperature and no heat flows between them.

Zeroth Law of Thermodynamics: If body A is in thermal equilibrium with body C, and body B is also in thermal equilibrium with body C, then A and B are in thermal equilibrium with each other.

This law forms the basis of temperature measurement and explains how thermometers work.

Heat, Work and Internal Energy

A thermodynamic system can gain or lose energy through heat transfer and work done.

Work Done by a Gas

When a gas expands or compresses inside a cylinder, work is performed due to change in volume.

$$W=\int_{V_1}^{V_2}P\,dV$$

• During expansion, work done by the gas is positive.
• During compression, work done by the gas is negative.
• On a PV diagram, work is represented by the area under the curve.

JEE Tip: In JEE convention, heat supplied to the system is positive and work done by the system is positive.

First Law of Thermodynamics

The first law represents conservation of energy in thermodynamic systems. Heat supplied to a system is used to increase internal energy and perform work.

$$Q=\Delta U+W$$

Where:

• $$Q$$ = heat supplied
• $$\Delta U$$ = change in internal energy
• $$W$$ = work done by system

Worked Example

A gas absorbs 500 J heat and performs 200 J work on the surroundings. Find the change in internal energy.

$$Q=\Delta U+W$$

$$500=\Delta U+200$$

$$\Delta U=300J$$

The internal energy increases by 300 J.

Internal Energy of Ideal Gas

For an ideal gas, internal energy depends only on temperature.

$$U=\frac{f}{2}nRT$$

The change in internal energy is:

$$\Delta U=nC_v\Delta T=\frac{f}{2}nR\Delta T$$

Here, $$f$$ represents degrees of freedom of the gas molecules.

Thermodynamic Processes

A thermodynamic process describes the transition of a system from one state to another. Different constraints produce different types of processes.

Isothermal Process

An isothermal process occurs at constant temperature.

• Temperature remains constant.
• For ideal gas, $$\Delta U=0$$.
• Heat supplied is completely converted into work.

$$PV=\text{constant}$$

$$W=nRT\ln\frac{V_2}{V_1}$$

Worked Example

Two moles of an ideal gas expand isothermally at 300 K from volume V to 3V. Find work done.

$$W=nRT\ln\frac{V_2}{V_1}$$

$$W=2(8.314)(300)\ln3$$

$$W=5482J$$

Adiabatic Process

An adiabatic process occurs when no heat exchange takes place between the system and surroundings.

$$Q=0$$

$$PV^\gamma=\text{constant}$$

Other relations:

$$TV^{\gamma-1}=\text{constant}$$

$$T^\gamma P^{1-\gamma}=\text{constant}$$

• Expansion causes cooling.
• Compression causes heating.
• The adiabatic curve is steeper than the isothermal curve.

Isobaric Process

An isobaric process occurs at constant pressure.

$$W=P\Delta V=nR\Delta T$$

$$Q=nC_p\Delta T$$

Isochoric Process

An isochoric process occurs at constant volume.

• Volume remains constant.
• No work is performed.

$$W=0$$

$$Q=\Delta U=nC_v\Delta T$$

Comparison of Thermodynamic Processes

PV Diagrams, Cyclic Processes and Second Law

PV Diagrams

A PV diagram represents the change in pressure and volume during a thermodynamic process.

• The area under the curve represents work done.
• In a cyclic process, the system returns to its initial state.
• For a complete cycle:

$$\Delta U=0$$

The net work done is equal to the area enclosed by the cycle.

• Clockwise cycle → Positive work output (heat engine).
• Anticlockwise cycle → Refrigerator or heat pump.

Second Law of Thermodynamics

The first law explains energy conservation, but the second law explains the direction of natural processes.

Kelvin-Planck Statement: No heat engine can convert all absorbed heat into work.

Clausius Statement: Heat cannot flow from a colder body to a hotter body without external work.

Carnot Engine, Refrigerator and Entropy

Carnot Engine

The Carnot engine is an ideal heat engine that works on a completely reversible cycle. It represents the maximum possible efficiency of an engine operating between two temperatures.

The Carnot cycle consists of:

• Isothermal expansion
• Adiabatic expansion
• Isothermal compression
• Adiabatic compression

$$\eta=1-\frac{T_C}{T_H}$$

Other forms:

$$\eta=1-\frac{Q_C}{Q_H}=\frac{W}{Q_H}$$

Here:

• $$T_H$$ = temperature of hot reservoir
• $$T_C$$ = temperature of cold reservoir
• $$Q_H$$ = heat absorbed
• $$Q_C$$ = heat rejected

Worked Example

A Carnot engine works between 600 K and 300 K and absorbs 1000 J heat. Find efficiency and work output.

$$\eta=1-\frac{300}{600}$$

$$\eta=0.5$$

Efficiency = 50%

$$W=\eta Q_H$$

$$W=0.5\times1000$$

$$W=500J$$

Refrigerator and Heat Pump

A refrigerator works as a heat engine in reverse. It uses external work to transfer heat from a colder region to a hotter region.

$$COP=\frac{Q_C}{W}$$

For an ideal refrigerator:

$$COP=\frac{T_C}{T_H-T_C}$$

Entropy

Entropy is a measure of randomness or disorder in a system. The second law states that entropy of an isolated system never decreases.

$$\Delta S=\frac{Q_{rev}}{T}$$

For an ideal gas:

$$\Delta S=nC_v\ln\frac{T_2}{T_1}+nR\ln\frac{V_2}{V_1}$$

Kinetic Theory of Gases

Kinetic theory explains the behaviour of gases by considering molecules in continuous random motion. Pressure and temperature arise due to molecular collisions.

Ideal Gas Equation

The ideal gas equation relates pressure, volume, temperature and number of molecules.

$$PV=nRT=Nk_BT$$

Where:

• $$n$$ = number of moles
• $$N$$ = number of molecules
• $$R$$ = universal gas constant
• $$k_B$$ = Boltzmann constant

The relation between both constants is:

$$R=N_Ak_B$$

Pressure from Molecular Motion

Pressure is produced due to collisions of gas molecules with container walls.

$$P=\frac{1}{3}\rho v_{rms}^{2}$$

where $$\rho$$ represents density of the gas.

Kinetic Energy and Temperature

The average kinetic energy of gas molecules depends only on temperature.

$$\frac{1}{2}mv_{rms}^{2}=\frac{3}{2}k_BT$$

For one mole:

$$KE=\frac{3}{2}RT$$

For n moles:

$$KE_{total}=\frac{3}{2}nRT$$

Molecular Speeds

The order of speeds is:

$$v_{mp}

JEE Important Points, Common Mistakes and Quick Revision

Points JEE Repeatedly Tests

• Heat, work and internal energy are different forms of energy transfer and storage.
• Internal energy of an ideal gas depends only on temperature.
• Work done by a gas is positive during expansion and negative during compression.
• The first law of thermodynamics represents conservation of energy.
• In an isothermal process, temperature and internal energy remain constant for an ideal gas.
• In an adiabatic process, no heat exchange occurs between the system and surroundings.
• The area under a PV curve represents work done.
• In a cyclic process, the final state is the same as the initial state, so net change in internal energy is zero.
• Carnot engine gives the maximum possible efficiency between two temperatures.
• Efficiency of a heat engine can never be 100% because some heat must be rejected.
• Entropy of an isolated system always increases or remains constant.
• Gas pressure is produced due to collisions of molecules with container walls.
• Average kinetic energy of molecules depends only on absolute temperature.

• Degrees of freedom determine the energy stored by gas molecules.
• For all gases, $$C_p$$ is greater than $$C_v$$.

Common Mistakes to Avoid

1. Wrong sign convention: Always remember whether work is done by the system or on the system.
2. Assuming heat and temperature are the same: Heat is energy transfer, while temperature measures thermal state.
3. Using ideal gas relations for non-ideal conditions: Kinetic theory assumptions apply mainly to ideal gases.
4. Forgetting that internal energy depends only on temperature: For an ideal gas, volume and pressure do not directly affect internal energy.
5. Confusing isothermal and adiabatic processes: Isothermal has constant temperature, while adiabatic has zero heat exchange.
6. Using Celsius instead of Kelvin: Thermodynamic equations require absolute temperature.
7. Mixing efficiency and coefficient of performance: Heat engines and refrigerators use different performance measures.
8. Ignoring degrees of freedom: Specific heat calculations depend on the number of independent energy modes.
9. Using incorrect molecular speed relation: RMS speed is always greater than average and most probable speeds.

Quick Revision Notes for Thermodynamics and Kinetic Theory

• Thermodynamics explains energy transfer through heat and work.
• The zeroth law defines thermal equilibrium and temperature measurement.
• The first law is based on conservation of energy.
• Internal energy of an ideal gas depends only on temperature.
• Isothermal processes occur at constant temperature.
• Adiabatic processes occur without heat exchange.
• Isobaric processes occur at constant pressure.
• Isochoric processes occur at constant volume.
• PV diagrams help calculate work done in thermodynamic processes.
• Carnot engine represents maximum possible heat engine efficiency.
• Entropy measures disorder and direction of natural processes.
• Kinetic theory explains gas behaviour through molecular motion.
• Pressure arises due to molecular collisions.
• Temperature represents average kinetic energy of molecules.
• Degrees of freedom determine molecular energy distribution.
• Specific heats of gases depend on molecular structure.