Question: An aircraft engine takes in \(9000\;J\) of heat and discards \(6400\;J\) each cycle. (a) What is the mechanical work output of the engine during one cycle? (b) What is the thermal efficiency of the engine?

Aircraft engine takes amount of heat, \({Q_H} = 9000\;{\rm{J}}\)

The amount of heat discarded,\({Q_C} = - 6400\;{\rm{J}}\)

The mechanical work done of the is defined as the sum of the heat must be supplied and discarded heat.

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

\(W = {Q_H} + {Q_c}\) …… (i)

Here, \({Q_c}\)is the discarded heat and\({Q_H}\)is the heat that must be supplied to diesel engine.

Calculate the mechanical work output.

Substitute \( - 6400\;{\rm{J}}\) for \({Q_c}\) and \(9000\;{\rm{J}}\) for \({Q_H}\) into equation (i).

\(\begin{array}{l}W = 9000 + \left( { - 6400} \right)\\W = 9000 - 6400\\W = 2600\;{\rm{J}}\end{array}\)

Hence the mechanical work out of the engine is \(2600\;{\rm{J}}\).