Thermodynamics
Thermodynamics in the HSC paper is primarily about the first law applied to the four standard processes, work done by a gas, cyclic processes, and the efficiency of heat engines and refrigerators. Carnot-cycle reasoning and the second law statements are frequent short-answer questions.
Core rules
- Zeroth law defines temperature and justifies thermometers; the first law is ΔU = Q − W, with W done by the gas.
- Isothermal (T constant): ΔU = 0, W = nRT ln(V₂/V₁) = nRT ln(P₁/P₂).
- Adiabatic (Q = 0): W = (P₁V₁ − P₂V₂)/(γ − 1) and PV^γ = constant, TV^(γ−1) = constant.
- Isobaric: W = PΔV = nRΔT, Q = nC(P)ΔT. Isochoric: W = 0, Q = nC(V)ΔT.
- Cyclic process: ΔU = 0 over a full cycle, so Q(net) = W(net), the area enclosed on a P-V diagram.
- Heat engine efficiency η = W/Q₁ = 1 − Q₂/Q₁. Carnot: η = 1 − T₂/T₁, using kelvin.
- Refrigerator/heat pump: COP = Q₂/W = T₂/(T₁ − T₂) for the ideal case.
- Second law: no engine can convert all heat from a single reservoir into work, and heat cannot flow spontaneously from cold to hot.
Worked example
A Carnot engine works between 500 K and 300 K. η = 1 − 300/500 = 0.40, that is 40%. If it absorbs 1000 J per cycle from the source, W = 400 J and Q₂ = 600 J is rejected. Any real engine between the same reservoirs must do less work than this.
Traps
- Using the wrong sign for W, or forgetting that ΔU = 0 only for isothermal and complete-cycle paths of an ideal gas.
- Applying W = nRT ln(V₂/V₁) to an adiabatic process.
- Using Celsius temperatures in the Carnot efficiency formula - kelvin is mandatory.