Energy and Efficiency

Waste Heat

what is not converted to work

Waste heat is the part of the heat input that must be rejected rather than converted to useful work. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Not all heat becomes work

The heat input is 30 joules, but useful work is only 12 joules.

Qin=30 JWout=12 JQ_{\text{in}} = 30\ \text{J}\qquad W_{\text{out}} = 12\ \text{J}
Waste heat budgetWaste is the part of the heat input not converted to work.30 Jinput12 Jwork18 Jwaste

Find the waste heat

Waste heat is the input heat minus the useful work.

Qwaste=Qin−WoutQ_{\text{waste}} = Q_{\text{in}} - W_{\text{out}}

Compute the rejected heat

Subtract 12 joules from 30 joules. The waste heat is 18 joules.

Qwaste=30 J−12 J=18 JQ_{\text{waste}} = 30\ \text{J} - 12\ \text{J} = 18\ \text{J}
Waste heat budgetWaste is the part of the heat input not converted to work.30 Jinput12 Jwork18 Jwaste

More work leaves less waste at fixed input

Hold the heat input at 30 joules. The diagram shows the middle row; converting more to work leaves less waste heat.

QinWoutQwaste30 J6 J24 J30 J12 J18 J30 J18 J12 J\begin{array}{c|c|c}Q_{\text{in}}&W_{\text{out}}&Q_{\text{waste}}\\30\ \text{J}&6\ \text{J}&24\ \text{J}\\30\ \text{J}&12\ \text{J}&18\ \text{J}\\30\ \text{J}&18\ \text{J}&12\ \text{J}\\\end{array}
Waste heat budgetThe middle table row is the checked diagram.30 Jinput12 Jwork18 Jwaste

More input leaves more waste if work is fixed

Now hold useful work at 12 joules. A larger heat input must send the extra energy somewhere, so the waste row grows.

QinWoutQwaste24 J12 J12 J30 J12 J18 J36 J12 J24 J\begin{array}{c|c|c}Q_{\text{in}}&W_{\text{out}}&Q_{\text{waste}}\\24\ \text{J}&12\ \text{J}&12\ \text{J}\\30\ \text{J}&12\ \text{J}&18\ \text{J}\\36\ \text{J}&12\ \text{J}&24\ \text{J}\\\end{array}
Waste heat budgetThe middle table row is the checked diagram.30 Jinput12 Jwork18 Jwaste