An electrical generating plant operates at a boiler temperature of 225°C and exhausts the unused heat into a nearby river at 25.0°C.If the generating plant has a power output of 850 megawatts (MW)and if the actual efficiency is 3/4 the theoretical efficiency,how much heat per second must be delivered to the boiler? (0°C = 273 K)

Question

Quizplus · Accepted Answer

The theoretical efficiency of a heat engine operating between two temperatures is given by the Carnot efficiency, $\eta = 1 - \frac{T_c}{T_h}$, where $T_c$ and $T_h$ are the cold and hot reservoir temperatures in Kelvin, respectively. For this plant, $T_h = 225°C + 273 = 498K$ and $T_c = 25°C + 273 = 298K$. Thus, $\eta = 1 - \frac{298}{498} = 0.4$ or 40%. The actual efficiency is $0.75 \times 0.4 = 0.3$ or 30%. Given the power output (work done) is 850 MW and using the efficiency equation $\eta = \frac{W}{Q_h}$, where $W$ is the work done and $Q_h$ is the heat supplied, we can solve for $Q_h$: $0.3 = \frac{850}{Q_h}$, giving $Q_h = \frac{850}{0.3} = 2833.33$ MW, which rounds to 2830 MW or option D.

An Electrical Generating Plant Operates at a Boiler Temperature of 225°C