Thermodynamics, Heat Transfer, and Energy Systems
Thermodynamics questions test property relationships and cycle analysis; heat transfer questions test which mode dominates and how to build a thermal resistance network.
Core rules
- Steady-flow first law: Q − W = ΔH + ΔKE + ΔPE. For a closed system, Q − W = ΔU.
- Ideal gas: pV = mRT with R = 8.314/M kJ/kg·K; cp − cv = R and k = cp/cv. Reversible adiabatic relations use pV^k = constant.
- Entropy: Δs = ∫dQ_rev/T. Carnot efficiency is η = 1 − T_L/T_H, using absolute temperatures.
- Rankine cycle: boiler, turbine, condenser, pump. Brayton cycle: isentropic compression and expansion with constant-pressure heat addition.
- Conduction q = kAΔT/L with R = L/(kA); convection q = hAΔT with R = 1/(hA); radiation q = εσA(T_s⁴ − T_sur⁴).
- Heat exchangers: q = UA(LMTD) for counterflow or parallel flow.
Worked example
A 0.1 m thick wall with k = 0.5 W/m·K and A = 10 m² has faces at 30 °C and 10 °C. q = kAΔT/L = 0.5 × 10 × 20/0.1 = 1000 W. Adding a second layer in series adds resistance, and the temperature drop across each layer is proportional to its share of the total resistance.
Traps
- Using °C in the ideal gas law, in Carnot efficiency, or in the radiation equation.
- Reversing the sign convention so work or heat comes out with the wrong sign.
- Substituting an arithmetic mean temperature difference where the LMTD is required.
- Treating COP as an efficiency that must stay below 1; a heat pump COP routinely exceeds 1.