Thermodynamics & Kinetic Theory
Laws of thermodynamics, heat engines, Carnot cycle, and kinetic theory of gases
Key Concepts
- First law of thermodynamics: ΔU = Q − W (energy conservation)
- Processes: isothermal (ΔU = 0), adiabatic (Q = 0), isochoric (W = 0), isobaric (W = PΔV)
- Carnot engine has the maximum possible efficiency between two temperatures
- Kinetic theory: absolute temperature is proportional to mean kinetic energy
- Equipartition: each degree of freedom contributes ½kT of energy
Important Formulae
| First law | ΔU = Q − W |
| Carnot efficiency | η = 1 − T_L/T_H |
| Specific heats | C_p − C_v = R; γ = C_p/C_v |
| Isothermal work | W = nRT ln(V₂/V₁) |
| Adiabatic relation | PV^γ = constant |
| RMS speed | v_rms = √(3RT/M) |
Quick Tips
- γ = 5/3 for monatomic gases and 7/5 for diatomic gases.
- In any complete cyclic process ΔU = 0, so Q = W.
- Work done by the gas is the area under the P–V curve.
Sample Practice Questions
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In an isochoric (constant volume) process, the work done by the gas is:
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Answer: Zero
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The ratio of specific heats γ for a monatomic ideal gas is:
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Answer: 5/3
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A Carnot engine operates between 600 K and 300 K. Its efficiency is:
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Answer: 50%
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The first law of thermodynamics is expressed as:
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Answer: ΔU = Q − W
Practice Questions
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What are the key concepts in Thermodynamics & Kinetic Theory for JEE?
First law of thermodynamics: ΔU = Q − W (energy conservation); Processes: isothermal (ΔU = 0), adiabatic (Q = 0), isochoric (W = 0), isobaric (W = PΔV); Carnot engine has the maximum possible efficiency between two temperatures; Kinetic theory: absolute temperature is proportional to mean kinetic energy; Equipartition: each degree of freedom contributes ½kT of energy.
Which formulae are important for Thermodynamics & Kinetic Theory in JEE?
First law: ΔU = Q − W; Carnot efficiency: η = 1 − T_L/T_H; Specific heats: C_p − C_v = R; γ = C_p/C_v; Isothermal work: W = nRT ln(V₂/V₁); Adiabatic relation: PV^γ = constant; RMS speed: v_rms = √(3RT/M).
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