Chapter 15, Problem 59GP

To determine

The efficiency of the engine.

Answer to Problem 59GP

The efficiency of the engine is 24%.

Explanation of Solution

Given info:

The energy released in the burning of gasoline is, $E=3\times {10}^4\text{kcal}/\text{gal}$ .

The average of the car is, $q=41\text{km}/\text{gal}$ .

The speed of the car is, $v=90\text{km}/\text{h}$ .

The power required by the car is, $P=25\text{hp}=\left(25\text{hp}\right)\left(\frac{746\text{J}/\text{s}}{1\text{hp}}\right)=18650\text{J}/\text{s}$ .

Formula Used:

The expression to calculate the power of car is,

  $P_c=\frac{Ev}{q}$

The expression to calculate the efficiency of the engine is,

  $\eta =\frac{P}{P_c}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}{P}_c=\frac{\left(3\times {10}^4\text{kcal}/\text{gal}\right)\left(90\text{km}/\text{h}\right)}{41\text{km}/\text{gal}}\\ =6.59\times {10}^4\text{kcal}/\text{h}\\ =\left(6.59\times {10}^4\text{kcal}/\text{h}\right)\left(\frac{4186\text{J}}{1\text{kcal}}\times \frac{1\text{h}}{3600\text{s}}\right)\\ =7.66\times {10}^4\text{J}/\text{s}\end{array}$

Substitute all the values in the above expression.

  $\begin{array}{c}\eta =\frac{18650\text{J}/\text{s}}{7.66\times {10}^4\text{J}/\text{s}}\\ =0.24\\ =24\%\end{array}$

Conclusion:

Thus, the efficiency of the engine is 24%.