Thermodynamics and Heat Transfer
What you must command
The laws of thermodynamics, properties of ideal gases and steam, thermodynamic processes (isothermal, adiabatic, isobaric, isochoric, polytropic), cycles (Carnot, Otto, Diesel, Rankine, Brayton), and the three modes of heat transfer - conduction, convection, radiation - with their governing equations.
Traps that appear in questions
- Sign convention: work done by the system is positive in the convention used by most engineering texts; be consistent.
- Adiabatic vs. isothermal: adiabatic uses pV^γ = constant; isothermal uses pV = constant. Mixing them changes the answer substantially.
- Carnot efficiency depends only on absolute temperatures: η = 1 − T_cold/T_hot. Using Celsius gives nonsense.
- Steam tables: use enthalpy for flow processes, internal energy for closed systems; superheated vs. saturated states.
- Radiation: Stefan–Boltzmann uses absolute temperature to the fourth power; a small temperature change has a large effect.
- Conduction: thermal resistance L/(kA) adds in series like electrical resistance.
Worked rule of thumb
For a composite wall, total resistance R = Σ(L_i/(k_i A)); heat flow Q = ΔT/R. Example: a 100 mm brick wall (k = 0.7 W/m·K) and a 50 mm insulation layer (k = 0.04 W/m·K) over 1 m², with ΔT = 30 K. R = 0.1/0.7 + 0.05/0.04 = 0.143 + 1.25 = 1.393 K/W; Q = 30/1.393 ≈ 21.5 W. Notice the insulation dominates - a useful intuition for design questions.
For an ideal Otto cycle, η = 1 − r^(1−γ), where r is the compression ratio; higher r raises efficiency, which is why the question often asks about knock limits.