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) $=100\mathrm{\%}$. (b) $\approx 66\mathrm{\%}$. (c) $\approx 50\mathrm{\%}$. (d) $\approx 34\mathrm{\%}$.

(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 $e=1-\frac{Q_{\mathrm{L}}}{Q_{\mathrm{H}}}$.

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

Given data 

The lower temperature is $T_{\mathrm{L}}={300}^{\circ }\mathrm{C}=573\mathrm{K}$.

The higher temperature is $T_{\mathrm{H}}={600}^{\circ }\mathrm{C}=873\mathrm{K}$.

Calculation 

Now, the efficiency of the heat engine is:

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

Therefore, the efficiency of the heat engine is around $34\mathrm{\%}$.

Hence, the correct option is (d).