KinexiaLEARN PHYSICS

Carnot Efficiency — Steam Power Plant (Worked Example)

Medium
Problem

A steam power plant operates between 800 K (boiler) and 300 K (cooling). What is its maximum possible (Carnot) efficiency?

Given

  • Th = 800 K

  • Tc = 300 K

Find

The Carnot efficiency η.

Principle

No heat engine can beat η = 1 − Tc/Th — the second law's hard ceiling, with absolute temperatures.

Formula

Solution

  1. Write the formula: η=1−Tc/Th\eta = 1 - T_c/T_h

  2. Substitute: η=1−300/800\eta = 1 - 300/800

  3. Calculate: η=1−0.375=0.625\eta = 1 - 0.375 = 0.625

0.625 (62.5%)

Unit check

K ÷ K — dimensionless, correct.

What this means physically

62.5% is the absolute ceiling; real plants manage ~40% after friction, heat loss and non-ideal cycles. The gap between Carnot and reality is engineering's battleground.

Common mistake

Using Celsius: 1 − 27/527 gives nonsense. Carnot needs kelvin — convert °C + 273 first, always.