Question

An engine does 10 J of work and exhausts 25 J of waste heat during each cycle.

what is the thermal efficiency?

I did it like this...
eff =
`(work)/(Qh)= (10J)/(15J)` = 0.67 = 67%

But my homework said it was incorrect

So i tried it this way
eff =
`(work)/(Qh)= (10J)/(25J)` = 0.4 = 40%

But that is also incorrect, so what am i doing wrong?

Answer 1

The thermal efficiency is defined as follows


`\eta = 1 - \frac{Q_{\text{out}}}{Q_\text{in}}`,

and the energy which is put into the system is


`Q_{\text{in}} = W_\text{out} + Q_\text{out}`.

In your case
`Q_\text{in} = 25 \text{ J},W_\text{out}=10 \text{ J}.`

So
`Q_\text{out}=10 \text{ J}` which gives an efficiency of


`\eta = 1 - \frac{10 \text{ J}}{25 \text { J}} = 0.6 = 60 \%`.