Thermodynamics
Thermodynamics
The exam tests property relations, the first and second laws, gas cycles, steam cycles, and combustion basics. Sign conventions and absolute temperatures are common mark-losers.
Core rules
- Closed system: Q − W = ΔU. Steady-flow: q − w = Δh + Δke + Δpe. Use the convention that heat into the system is positive and work done by the system is positive, then state it explicitly.
- Second law: ΔS_universe ≥ 0. Carnot efficiency η = 1 − T_L/T_H only with absolute temperatures. Entropy change for an ideal gas: Δs = c_p ln(T₂/T₁) − R ln(p₂/p₁).
- Ideal gas: pV = mRT; c_p − c_v = R; γ = c_p/c_v. For air, R = 0.287 kJ/kg·K.
- Rankine cycle: η = (w_t − w_p)/q_in. Reheat and regeneration raise the mean temperature of heat addition; they do not beat the Carnot limit.
Worked example
A heat engine receives 1000 kJ from a 600 K reservoir and rejects heat to 300 K. Carnot η = 1 − 300/600 = 0.50, so maximum work = 500 kJ and minimum rejection = 500 kJ. If the actual engine rejects 600 kJ, its work is 400 kJ and η = 40%. The entropy generated per cycle is ΔS_univ = −1000/600 + 600/300 = −1.667 + 2.000 = +0.333 kJ/K, confirming irreversibility.
Traps
Using °C in Carnot or entropy relations; reversing the work sign; treating isentropic efficiency as a cycle efficiency; ignoring pump work in a Rankine cycle; and assuming a real gas follows pV = mRT at high pressure.