Chapter 24, Problem 28A

Calculate the ideal efficiency of a steam turbine that has a hot reservoir of $112°C$ high-pressure steam and a sink at $27°C$.

To determine

The ideal efficiency of a steam turbine.

Answer to Problem 28A

The ideal efficiency of a steam turbine that has a hot reservoir of $112°\text{C}$ high pressure steam and a sink at $\text{27}°\text{C}$ is found to be $22\%$ .

Explanation of Solution

Given:

The temperature of the hot reservoir

  $T_{\text{hot}}=112°\text{C}$

The temperature of the cold reservoir

  $T_{\text{cold}}=\text{27}°\text{C}$

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:

Express the temperatures of the hot reservoir and the sink in Kelvin.

  $\begin{array}{l}{T}_{\text{hot}}=112°\text{C}+273=385\text{ K}\\ T_{\text{cold}}=\text{27}°\text{C}+273=300\text{ K}\end{array}$

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

  $\begin{array}{c}\text{Ideal efficiency}=\frac{T_{\text{hot}}-T_{\text{cold}}}{T_{\text{hot}}}\\ =\frac{\left(385\text{ K}\right)-\left(300\text{ K}\right)}{\left(385\text{ K}\right)}\\ =0.22\end{array}$

Express the efficiency of the turbine in percentage.

  $\begin{array}{c}\text{Ideal efficiency}=0.22\times 100\%\\ =22\%\end{array}$

Conclusion:

Thus, ideal efficiency of a steam turbine that has a hot reservoir of $112°\text{C}$ high pressure steam and a sink at $\text{27}°\text{C}$ is found to be $22\%$ .