Chapter 24, Problem 51A

What is the ideal efficiency of an automobile engine wherein fuel is heated to 2700 K and the outdoor air is 300 K?

To determine

The ideal efficiency of an automobile engine.

Answer to Problem 51A

The ideal efficiency of an automobile engine, wherein the fuel is heated to 2700 K and temperature of the outdoor air is 300 K is found to be $\text{89\%}$ .

Explanation of Solution

Given:

The temperature of the Fuel

  $T_{\text{hot}}=2700\text{ K}$

The temperature of the outside air

  $T_{\text{cold}}=300\text{ K}$

Formula used:

The ideal efficiency of a heat engine is given by the expression,

  $\text{Ideal efficiency}=\frac{T_{\text{hot}}-T_{\text{cold}}}{T_{\text{hot}}}$

Calculation:

Substitute the values of the variables in the formula and calculate the ideal efficiency.

  $\begin{array}{c}\text{Ideal efficiency}=\frac{T_{\text{hot}}-T_{\text{cold}}}{T_{\text{hot}}}\\ =\frac{\left(2700\text{ K}\right)-\left(300\text{ K}\right)}{\left(2700\text{ K}\right)}\\ =0.89\end{array}$

Express the efficiency of the automobile engine in percentage.

  $\begin{array}{c}\text{Ideal efficiency}=0.89\times 100\%\\ =89\%\end{array}$

Conclusion:

Thus, the ideal efficiency of an automobile engine, wherein the fuel is heated to 2700 K and temperature of the outdoor air is 300 K is found to be $\text{89\%}$ .