Question

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?

Short answer

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

Step-by-step solution

Understanding the working of the heat 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.

Identification of given data

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 \(W = 9200{\rm{ J}}\).

Determination of the efficiency of the heat engine

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 \(8.79\% \).