KinexiaLEARN PHYSICS

Carnot Efficiency — Solar Thermal Plant (Worked Example)

Easy
Problem

A solar thermal plant heats fluid to 600 K and rejects heat at 300 K. What is its maximum theoretical efficiency?

Given

  • Th = 600 K

  • Tc = 300 K

Find

The Carnot efficiency η.

Principle

η = 1 − Tc/Th — modest temperatures mean a modest ceiling.

Formula

Solution

  1. Substitute: η=1−300/600\eta = 1 - 300/600

  2. Note: Tc/Th=0.5T_c/T_h = 0.5 here, so exactly half the heat must be rejected even ideally

  3. Calculate: η=1−0.5=0.50\eta = 1 - 0.5 = 0.50

0.50 (50%)

Unit check

Dimensionless — correct.

What this means physically

50% maximum; real solar-thermal plants get ~20%. This is why photovoltaic panels (no heat cycle) often win economically despite their own limits.

Common mistake

Confusing collector efficiency with Carnot. Carnot limits only the heat-to-work step — the mirrors' optical losses are separate.