Question

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

Short answer

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

Step-by-step solution

Understanding the maximum efficiency of the heat engine

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.

Identification of given data

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 \({T_{\rm{L}}} = 345^\circ {\rm{C}} = \left( {345^\circ {\rm{C}} + 273} \right){\rm{ K}} = 618{\rm{ K}}\).

Determination of the maximum efficiency of the heat engine

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 \(25.81\% \).