Question

A heat engine operates between a high temperature of about 600°C and a low temperature of about 300°C. What is the maximum theoretical efficiency for this engine?

(a) \( = 100\% \). (b) \( \approx 66\% \). (c) \( \approx 50\% \). (d) \( \approx 34\% \).

(e) Cannot be determined from the given information.

Short answer

The correct option is (d).

Step-by-step solution

Concepts

The efficiency of the heat engine is \(e = 1 - \frac{{{Q_{\rm{L}}}}}{{{Q_{\rm{H}}}}}\).

The most used form of the efficiency of the heat engine is\(e = 1 - \frac{{{T_{\rm{L}}}}}{{{T_{\rm{H}}}}}\).

Given data 

The lower temperature is \({T_{\rm{L}}} = {300^ \circ }{\rm{C}} = 573\;{\rm{K}}\).

The higher temperature is \({T_{\rm{H}}} = {600^ \circ }{\rm{C}} = 873\;{\rm{K}}\).

Calculation 

Now, the efficiency of the heat engine is:

\(\begin{array}{c}e = \left( {1 - \frac{{{T_{\rm{L}}}}}{{{T_{\rm{H}}}}}} \right) \times 100\% \\ = \left( {1 - \frac{{573\;{\rm{K}}}}{{873\;{\rm{K}}}}} \right) \times 100\% \\ \approx 34\% \end{array}\)

Therefore, the efficiency of the heat engine is around \(34\% \).

Hence, the correct option is (d).