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Carnot Efficiency — Diesel Engine (Worked Example)

Medium
Problem

A diesel engine's combustion reaches 2200 K while exhaust leaves near 300 K. What is the Carnot efficiency limit?

Given

  • Th = 2200 K

  • Tc = 300 K

Find

The Carnot efficiency η.

Principle

Higher Th raises the ceiling: η = 1 − Tc/Th rewards hot combustion.

Formula

Solution

  1. Substitute: η=1−300/2200\eta = 1 - 300/2200

  2. Note: temperatures must be absolute — convert any Celsius values by adding 273 before dividing

  3. Calculate: η=1−0.1364=0.8636\eta = 1 - 0.1364 = 0.8636

0.864 (86.4%)

Unit check

Dimensionless — correct.

What this means physically

86.4% theoretical — yet real diesels achieve ~45%. Materials melt long before ideal cycles, so engineers chase the limit with turbos and better cooling instead.

Common mistake

Thinking real engines approach Carnot. Friction, finite-time cycles and heat leaks keep reality far below — Carnot is a ceiling, not a target.