Thermodynamics, Fluid Mechanics, and Heat Transfer
Domain scope
This domain covers the first and second laws, ideal-gas relations, entropy, Bernoulli and continuity, Reynolds number, conduction, convection, radiation, and heat-exchanger basics. Expect unit-heavy numerical questions.
Core rules
- First law for a steady-flow control volume: q − w = Δh + Δke + Δpe.
- Ideal gas: pV = mRT; use absolute pressure and kelvin.
- Carnot efficiency: η = 1 − T_C/T_H, with both temperatures in kelvin.
- Continuity: A₁V₁ = A₂V₂ for incompressible flow.
- Bernoulli: p/ρg + V²/2g + z = constant along a streamline for steady, incompressible, frictionless flow.
- Reynolds number Re = ρVD/μ; low Re is laminar, high Re turbulent.
- Conduction: q = kAΔT/L. Radiation: q = εσA(T_s⁴ − T_sur⁴).
Worked example
A Carnot engine operates between 600 K and 300 K and receives 1000 kJ of heat. η = 1 − 300/600 = 0.50, so work output is 0.50×1000 = 500 kJ. The remaining 500 kJ is rejected. If the same reservoir temperatures were mistakenly used in Celsius, the result would be wrong because the ratio must use absolute temperature.
Traps
- Putting Celsius temperatures into Carnot or ideal-gas equations.
- Mixing gauge and absolute pressure.
- Applying Bernoulli across a pump or turbine where shaft work is present.
- Using the wrong sign convention for work and heat.
- Forgetting that radiation depends on absolute temperature to the fourth power.