KinexiaLEARN PHYSICS

Carnot Efficiency — Nuclear Plant (Worked Example)

Medium
Problem

A pressurized-water reactor makes steam at 590 K and condenses at 300 K. What is the Carnot efficiency limit?

Given

  • Th = 590 K

  • Tc = 300 K

Find

The Carnot efficiency η.

Principle

Nuclear plants are limited by modest steam temperatures: η = 1 − Tc/Th.

Formula

Solution

  1. Substitute: η=1−300/590\eta = 1 - 300/590

  2. Note: the ratio Tc/ThT_c/T_h sets the floor — no engineering can beat this second-law limit

  3. Calculate: η=1−0.5085=0.4915\eta = 1 - 0.5085 = 0.4915

0.492 (49.2%)

Unit check

Dimensionless — correct.

What this means physically

49.2% ceiling; actual plants run ~33%. The 'waste heat' warming rivers is thermodynamics, not poor design — the second law demands rejected heat.

Common mistake

Blaming nuclear technology for the low efficiency. Any heat source at 590 K faces the same 49% ceiling — coal, gas or uranium.