Thermodynamics, Heat Transfer, and Energy Systems
The energy block tests first and second law reasoning, power and refrigeration cycles, and the three heat transfer modes. Nezam items are usually one-step: an efficiency, a heat rate, a wall conductance, or a heat exchanger size.
Core rules
- First law for steady flow: q − w = Δh + Δke + Δpe. For a Rankine cycle, w_net = w_turbine − w_pump, and η = w_net/q_in.
- Carnot limit: η = 1 − T_L/T_H, always with absolute temperatures. COP_max for refrigeration = T_L/(T_H − T_L).
- Conduction: Q = kAΔT/L, with R = L/kA. Convection: Q = hAΔT, R = 1/hA. Resistances in series add.
- Heat exchangers: Q = UA·LMTD, with LMTD = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂) for counterflow.
- Combustion and boilers: heat rate in kJ/kWh = 3600/η; every 1% of efficiency is worth real fuel.
Worked example
Counterflow exchanger: hot stream 90 → 60 °C, cold stream 30 → 50 °C. ΔT₁ = 90 − 50 = 40 K, ΔT₂ = 60 − 30 = 30 K. LMTD = (40 − 30)/ln(40/30) = 10/0.2877 = 34.8 K. If UA = 2000 W/K, then Q = 2000 × 34.8 = 69.6 kW, which can be checked against the hot-stream capacity rate.
Traps
- Using °C in Carnot or entropy expressions where kelvin is mandatory.
- Applying the arithmetic mean temperature difference instead of the LMTD when the ratio exceeds about 2.
- Confusing kW of cooling with COP; COP = Q_evap/W_compressor, both in the same units.