Question:(I) What is the maximum efficiency of a heat engine whose operating temperatures are 560°C and 345°C?

The maximum efficiency of the heat engine is mainly dependent on the hot and cold reservoir's temperatures.

The Carnot engine provides the maximum achievable efficiency that a heat engine can attain. It is a reversible type of heat engine.

The given data can be listed below as:

• The temperature of the hot reservoir is\({T_{\rm{H}}} = 560^\circ {\rm{C}} = \left( {560^\circ {\rm{C}} + {\rm{273}}} \right){\rm{ K}} = 833{\rm{ K}}\).
• The temperature of the cold reservoir is \({T_{\rm{L}}} = 345^\circ {\rm{C}} = \left( {345^\circ {\rm{C}} + 273} \right){\rm{ K}} = 618{\rm{ K}}\).

The maximum efficiency of the heat engine can be expressed as:

\(e = \left( {1 - \frac{{{T_{\rm{L}}}}}{{{T_{\rm{H}}}}}} \right)\)

Substitute the values in the above equation.

\(\begin{aligned}{c}e &= \left( {1 - \frac{{618{\rm{ K}}}}{{833{\rm{ K}}}}} \right)\\ &= 0.2581\\ &= 0.2581 \times 100\% \\ &= 25.81\% \end{aligned}\)

Thus, the maximum efficiency of the heat engine is \(25.81\% \).