Chapter 15, Problem 64GP

(a)

To determine

The ratio of efficiency to maximum possible efficiency.

Answer to Problem 64GP

The ratio of efficiency to maximum possible efficiency is 28.1%.

Explanation of Solution

Given info:

The efficiency of the engine is, $\eta =15\%=0.15$ .

The temperature of the gas air mixture is, $T_h=495°\text{C}=\left(495°\text{C}+273\right)\text{K}=768\text{K}$ .

The temperature of the exhaust is, $T_l=85°\text{C}=\left(85°\text{C}+273\right)\text{K}=358\text{K}$ .

Formula Used:

The expression to calculate the maximum possible efficiency is,

  ${\eta }_{\max }=1-\frac{T_l}{T_h}$

The expression to calculate theratio of efficiency to maximum possible efficiency is,

  $x=\frac{\eta }{{\eta }_{\max }}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}{\eta }_{\max }=1-\frac{358\text{K}}{768\text{K}}\\ =0.534\end{array}$

Substitute all the values in the above expression.

  $\begin{array}{c}x=\frac{0.15}{0.534}\\ =0.281\\ =28.1\%\end{array}$

Conclusion:

Thus, the ratio of efficiency to maximum possible efficiency is 28.1%.

(b)

To determine

The power of the engine goes to moving the car and the heat goes to exhaust.

Answer to Problem 64GP

The power of the engine goes to moving the car is $7.46\times {10}^4\text{J}/\text{s}$ and the heat goes to exhaust is $1.522\times {10}^9\text{J}$ .

Explanation of Solution

Given info:

The power of the car engine is, $P=100\text{hp}=100\text{hp}\times \frac{746\text{W}}{1\text{hp}}=7.46\times {10}^4\text{W}\times \frac{1\text{J}/\text{s}}{1\text{W}}=7.46\times {10}^4\text{J}/\text{s}$ .

The time for the exhaust is, $t=1\text{h}=1\text{h}\times \frac{3600\text{s}}{1\text{h}}=3600\text{s}$ .

Formula Used:

The power of the engine goes to moving the car is same as the power of the engine.

The expression to calculate the heat goes to exhaust is,

  $Q=Pt\left(\frac{1}{\eta }-1\right)$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}Q=\left(7.46\times {10}^4\text{J}/\text{s}\right)\left(3600\text{}\text{s}\right)\left(\frac{1}{0.15}-1\right)\\ =1.522\times {10}^9\text{J}\end{array}$

Conclusion:

Thus, the power of the engine goes to moving the car is $7.46\times {10}^4\text{J}/\text{s}$ and the heat goes to exhaust is $1.522\times {10}^9\text{J}$ .