NapkinCalc

Physics 4 — Thermo & Fluids

Carnot — the law nobody beats

continues from lesson 2 — values defined earlier in the course stay live here

ELI5: no engine turning heat into work can beat η = 1 − T_cold/T_hot (kelvin). Not with better materials, not with any cleverness — it's a hard ceiling set by entropy itself. The bigger the temperature gap, the more work you can extract.

Thot=800T_{hot} = 800 combustion temperature (K)
Tcold=300T_{cold} = 300 exhaust to ambient (K)
ηcarnot=1−TcoldThot\eta_{carnot} = 1 - \frac{T_{cold}}{T_{hot}} = 0.62500.6250 62.5% — the unbeatable ceiling
✓ pass ηcarnot<1\eta_{carnot} < 1 a perfect (100%) heat engine is impossible — always

Real-world hook: the Carnot limit is why power plants run as hot as their turbines allow, why car engines top out near 35%, and why your fridge (a heat engine in reverse) costs energy to run.

Try it yourself: an engine runs between 600 K and 300 K. What is its maximum (Carnot) efficiency? (η = 1 − T_cold/T_hot.)

ηyou=1−300600\eta_{you} = 1 - \frac{300}{600} = 0.50000.5000 ✏️ Your turn: compute 1 − 300/600. (It comes out to 0.5 — a 50% ceiling.)
✓ pass abs(ηyou−1−300600)<10−9\mathrm{abs}\left(\eta_{you} - 1 - \frac{300}{600}\right) < 10^{-9} green when your Carnot efficiency is correct