Chapter 24, Problem 27A

Calculate the ideal efficiency of a ship’s boiler when steam comes out at 530 K, pushes through a steam turbine, and exits into a condenser that is kept at 290 K by circulating seawater.

To determine

The ideal efficiency of a ship’s boiler.

Answer to Problem 27A

The ideal efficiency of a ship’s boiler is $45\%$ .

Explanation of Solution

Given:

The temperature of the Steam from the boiler

  $T_{\text{hot}}=530\text{ K}$

The temperature of the steam exiting into the condenser

  $T_{\text{cold}}=290\text{ K}$

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.

  $\begin{array}{c}\text{Ideal efficiency}=\frac{T_{\text{hot}}-T_{\text{cold}}}{T_{\text{hot}}}\\ =\frac{\left(530\text{ K}\right)-\left(290\text{ K}\right)}{\left(530\text{ K}\right)}\\ =0.45\end{array}$

Express the efficiency of the engine in percentage.

$\begin{array}{c}\text{Ideal efficiency}=0.45\times 100\%\\ =45\%\end{array}$

Conclusion:

Thus, ideal efficiency of a ship’s boiler is $45\%$ .