Question

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?

Short answer

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

Step-by-step solution

Write the given data from the question.

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

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

Determine the formulas to calculate the heat must be supplied to engine per second.

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 heat must be supplied to engine per second.

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 \(642.85\;{\rm{KJ}}\).