Question: A gasoline engine has a power output of \(180\;kW\) (about \(241\;hp\)). Its thermal efficiency is \(28.0\% \). (a) How much heat must be supplied to the engine per second? (b) How much heat is discarded by the engine per second?

The power output,\(P = 180\;{\rm{kW}}\)

Thermal efficiency,\({\eta _{th}} = 28\% \)

The expression to calculate the mechanical output work per second is given as follows.

\(W = Pt\) …… (i)

Here,\(t\)is the time.

The expression to calculate the heat must be supplied to the engine is given as follows.

\({Q_H} = \frac{W}{{{\eta _{th}}}}\) …… (ii)

Calculate the mechanical output work per second.

Substitute \(180\;{\rm{kW}}\) for \(P\) and \(1\;{\rm{s}}\) for \(t\) into equation (i)

\(\begin{array}{l}W = \left( {180\;{\rm{kW}}} \right)\left( {1\;{\rm{s}}} \right)\\W = 180\;{\rm{KJ}}\end{array}\)

Calculate the heat must be supplied to engine.

Substitute \(180\;{\rm{kJ}}\) for \(W\) and \(28\% \) for \(\eta \) into equation (ii).

Hence the heat must be supplied to engine is \(642.85\;{\rm{KJ}}\).