KinexiaLEARN PHYSICS

Heat Engine Efficiency — Car Engine Energy Audit (Worked Example)

Medium
Problem

A gasoline engine absorbs 800 J of heat from burning fuel each cycle and expels 500 J to the exhaust and coolant. (a) How much work does it do per cycle? (b) What is its thermal efficiency?

Given

  • Q_h = 800 J (heat in)

  • Q_c = 500 J (heat out)

Find

Work W per cycle and efficiency η.

Principle

The first law demands energy balance: work out equals heat in minus heat rejected. Efficiency is the useful fraction.

Formula

Solution

  1. Work: W=Qh−Qc=800−500=300 JW = Q_h - Q_c = 800 - 500 = 300\ \mathrm{J}

  2. Efficiency: η=W/Qh=300/800\eta = W/Q_h = 300/800

  3. Calculate: η=0.375=37.5%\eta = 0.375 = 37.5\%

W = 300 J per cycle; η = 37.5%

Unit check

J − J = J; J/J is unitless, expressed as a percent. Consistent.

What this means physically

Only 37.5% of the fuel's energy moves the car — the rest heats the exhaust and radiator. Real car engines manage 25–30%; the second law guarantees no heat engine can ever reach 100%.

Common mistake

Computing efficiency as Q_c/Q_h (the wasted fraction, 62.5%) instead of W/Q_h. Efficiency always measures the useful output over the costly input.