Chapter 18, Problem 1OQ

To determine

The efficiency of the engine.

Answer to Problem 1OQ

Option (b) $0.288$.

Explanation of Solution

Write the formula to find the work done by the engine

    $W_{eng}=\left|Q_h\right|-\left|Q_c\right|$        (I)

Here, $W_{eng}$ is the work done by the engine, $Q_h$ is the energy absorbed by the hot reservoir and $Q_c$ is the energy absorbed by the cold reservoir.

Write the formula to find the efficiency of engine

    $e=\frac{W_{eng}}{Q_h}$        (II)

Here, $e$ is the thermal efficiency of the engine.

Conclusion:

Substitute $15.0\text{ kJ}$ for $W_{eng}$ and $37.0\text{ kJ}$ for $Q_c$ in equation (I) to find the value of $Q_h$

$\begin{array}{c}{Q}_h=15.0\text{ kJ}+37.0\text{ kJ}\\ =52.0\text{ kJ}\end{array}$

Substitute $15.0\text{ kJ}$ for $W_{eng}$ and $52.0\text{ kJ}$ for $Q_h$ in equation (II) to find the value of $e$

$\begin{array}{c}e=\frac{15.0\text{ kJ}}{52.0\text{ kJ}}\\ =0.288\\ =28.8\%\end{array}$

Thus, the efficiency of the energy is $0.288$. Option (b) is correct.