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Thermodynamics

Heat, laws of thermodynamics, Carnot engine

Key Concepts
  • Zeroth law: thermal equilibrium defines temperature
  • First law: ΔU = Q − W (energy conservation)
  • Second law: heat flows spontaneously from hot to cold; entropy increases
  • Isothermal: constant T (ΔU = 0); Adiabatic: Q = 0; Isochoric: W = 0; Isobaric: W = PΔV
  • Carnot engine has maximum efficiency for given temperature limits
Important Formulae
First law of thermodynamics ΔU = Q − W
Carnot efficiency η = 1 − T_L / T_H
Ideal gas law PV = nRT
Specific heats relation C_p − C_v = R; γ = C_p/C_v
Work in isothermal process W = nRT ln(V₂/V₁)
Work in adiabatic process W = (P₁V₁ − P₂V₂)/(γ − 1)
Quick Tips
  • γ = 5/3 for monatomic gas, 7/5 for diatomic gas.
  • Refrigerator COP = T_L / (T_H − T_L); heat pump COP = T_H / (T_H − T_L).
  • Entropy change ΔS = Q_rev / T; total entropy of universe never decreases.
Sample Practice Questions

  1. In an isochoric process:

    • No heat exchange
    • No work is done
    • Temperature is constant
    • Pressure is constant
    Show answer

    Answer: No work is done

  2. For a diatomic ideal gas, ratio γ = Cp/Cv:

    • 5/3
    • 7/5
    • 4/3
    • 3/2
    Show answer

    Answer: 7/5

  3. The relation PV^γ = constant applies to:

    • Isothermal process
    • Isochoric process
    • Isobaric process
    • Adiabatic process
    Show answer

    Answer: Adiabatic process

  4. Second law of thermodynamics rules out the possibility of:

    • Perpetual motion machine of first kind
    • Perpetual motion machine of second kind
    • Carnot engine
    • Refrigerator
    Show answer

    Answer: Perpetual motion machine of second kind

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Practice Questions

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