Heat and Thermodynamics
Core concepts
Expect questions on the zeroth, first, and second laws, thermodynamic processes (isothermal, adiabatic, isobaric, isochoric), heat capacities (Cp vs Cv), latent heat, thermal conduction, and entropy. You must know the Carnot efficiency and the Kelvin–Planck and Clausius statements of the second law. Kinetic theory links temperature to mean molecular kinetic energy.
Traps
- Using Cp where Cv is required, or forgetting Cp − Cv = R for an ideal gas.
- Treating an adiabatic process as isothermal - no heat exchange, but temperature changes.
- Forgetting that efficiency of a real engine is always less than Carnot's.
- Sign conventions in the first law: ΔU = Q − W (work done by the gas positive).
- Confusing heat with temperature; a large heat input may cause a small temperature rise if latent heat is involved.
Rule of thumb
For an ideal monatomic gas, γ = 5/3; for a diatomic gas at room temperature, γ = 7/5. Adiabatic relation: PV^γ = constant.
Worked example
A Carnot engine operates between 500 K and 300 K. Efficiency η = 1 − Tc/Th = 1 − 300/500 = 0.40, i.e. 40%. If it absorbs 1000 J per cycle from the hot reservoir, it does 400 J of work and rejects 600 J to the cold reservoir.