Q4E - University Physics with Modern Physics

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?

Step-by-Step Solution

Answer

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

Step 1: Write the given data from the question.

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

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

Step 2: 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)

Step 3: 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 \(642.85\;{\rm{KJ}}\).