Question

Question: A diesel engine performs \(2200\;J\)of mechanical work and discards \(4300\;J\) of heat each cycle. (a) How much heat must be supplied to the engine in each cycle? (b) What is the thermal efficiency of the engine?

Short answer

The amount of heat that must be supplied to the diesel engine is \(6500\;{\rm{J}}\).

Step-by-step solution

Determine the given data from the question.

The mechanical work done,\(W = 2200\;{\rm{J}}\)

Discarded heat energy,\({Q_c} = - 4300\;{\rm{J}}\)

Determine the formulas to calculate the heat must be supplied to engine in each cycle.

The mechanical work done is of the diesel engine is equal to the sum of the heat produce.

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

\({Q_H} = W - {Q_c}\) …… (i)

Here,\(W\)is the mechanical work and\({Q_c}\)is the discarded heat.

Calculate the heat must be supplied to engine in each cycle and thermal efficiency of engine.

Calculate the amount of heat that must be supplied to diesel engine.

Substitute \(2200\;{\rm{J}}\) for \(W\) and \( - 4300\;{\rm{J}}\) for \({Q_C}\) into equation (i).

\(\begin{array}{l}{Q_H} = 2200 - \left( { - 4300} \right)\\{Q_H} = 2200 + 4300\\{Q_H} = 6500\;{\rm{J}}\end{array}\)

Hence the amount of heat that must be supplied to the diesel engine is \(6500\;{\rm{J}}\).