Question

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?

Short answer

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

Step-by-step solution

Write the given data from the question.

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

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

Determine the formulas to calculate the mechanical work output.

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 of the 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 \(2600\;{\rm{J}}\).