Thermodynamics and Heat Transfer
Core content
Closed-system first law: Q − W = ΔU. The steady-flow energy equation adds flow work: q − w = Δh + Δke + Δpe. Learn ideal-gas relations (pv = RT, cp − cv = R, k = cp/cv) and the isentropic relations, for example T2/T1 = (p2/p1)^((k−1)/k). Second law: entropy of an isolated system never decreases; Carnot efficiency = 1 − Tc/Th with absolute temperatures, and it is the upper bound for any cycle between those reservoirs. Refrigerators and heat pumps are rated by COP = QL/Win, and COP_HP = COP_R + 1.
Heat transfer: conduction q = kAΔT/L; convection q = hAΔT; radiation q = εσA(Ts⁴ − Tsur⁴) with T in kelvin. Combined problems usually reduce to q = UAΔTlm, where ΔTlm = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2) for counter-flow or parallel-flow exchangers; apply the correction factor F for other arrangements.
Traps: mixing gauge and absolute pressure; using Celsius in radiation or Carnot; using cp where cv belongs in a constant-volume process; assuming a real compressor is isentropic (use isentropic efficiency); forgetting that ΔTlm collapses when ΔT1 = ΔT2, in which case use the arithmetic mean; and sign errors on work.
Worked rule of thumb: for a heat pump, ideal COP ≈ Th/(Th − Tc) in kelvin. A unit lifting heat to 45 °C from 5 °C has ideal COP = 318/40 ≈ 8, so a measured COP of 3 implies roughly 38 % of Carnot performance - a fast sanity check on any claimed COP.