Question:(I) A heat engine does 9200 J of work per cycle while absorbing 25.0 kcal of heat from a high-temperature reservoir. What is the efficiency of this engine?

The efficiency of the heat engine is dependent on the work done and the heat provided to the engine.

The heat can be absorbed from the higher temperature reservoir. The remaining heat can be rejected to the lower temperature reservoir. An engine changes the heat into the required mechanical work.

The given data can be listed below as:

• The heat absorbed by the heat engine is\({Q_{\rm{H}}} = 25{\rm{ kcal}}\left( {\frac{{4186{\rm{ J}}}}{{1{\rm{ kcal}}}}} \right) = 104650{\rm{ J}}\).
• The work done by the heat engine is \(W = 9200{\rm{ J}}\).

The efficiency of the heat engine can be expressed as:

\(e = \left( {\frac{W}{{{Q_{\rm{H}}}}}} \right)\)

Here,\({Q_{\rm{H}}}\)is the heat supplied to the heat engine.

Substitute the values in the above equation.

\(\begin{aligned}{c}e &= \left( {\frac{{9200{\rm{ J}}}}{{104650{\rm{ J}}}}} \right)\\e &= 0.0879\\e &= 0.0879 \times 100\% \\e &= 8.79\% \end{aligned}\)

Thus, the efficiency of the heat engine is \(8.79\% \).