Question

A heat engine does $200J$of work per cycle while exhausting $400J$of waste heat. What is the engine’s thermal efficiency?

Short answer

The thermal efficiency is$\frac{1}{3}\approx 33\mathrm{\%}$

Step-by-step solution

Definition of efficiency   

For a heat engine, thermal efficiency is the ratio of net heat output (for heating) to the energy input.

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Mathematical expression for efficiency

$\eta =\frac{outputenergy}{inputenergy}\times 100$...................(1)

Step :3  Sum of work done and waste heat

Output energy = 200 J .

Exhausted energy = 400 J .

Input energy = output energy + exhausted energy = 200 J + 400 J

input energy = 600 J

Substitute 200 J for output energy and 600 J for input energy

in equation (1)

$\eta =\frac{200\mathrm{J}}{200\mathrm{J}+400\mathrm{J}}$

$=\frac{1}{3}\approx 33\mathrm{\%}$