Question

An electric generator at a power plant produces energy by passing superheated steam from a high temperature container (reservoir), through a pipe connected to a series of fans, and then into a low temperature reservoir. As the steam passes across the blades of the fans some of the heat energy of the steam is transformed into mechanical energy, which turns the fans which in turn are connected to a generator, which in turn converts the mechanical energy into electrical energy.If the high temperature steam has a temperature of 387.9 K and the low temperature reservoir has a temperature of 117.9 K, what is the Carnot efficiency of this process?

Answer 1

The high temperature of the steam is

`T_H=387.9\text{ K}`

The lowest temperature of the steam is

`T_L=117.9\text{ K}`

The formula to calculate Carnot efficiency is

`\eta=\frac{T_H-T_L}{T_L_{}}`

Substituting the values, the Carnot efficiency will be

`\begin{gathered} \eta=(387.9-117.9)/(387.9) \\ =0.696\text{ }*100\text{ percentage} \\ =69.6\text{percentage} \end{gathered}`

The Carnot efficiency is 69.6 %.