An engineer uses a river (minimum temperature of 4$^{\circ}$C)to cool his electrical plant which heats water with a boiler operating at 220$^{\circ}$C.His boiler uses 420 kW of energy to heat water to steam.What is the maximum power output under ideal circumstances?
A) 230 kW
B) 186 kW
C) 330 kW
D) 416 kW

Question

Quizplus · Accepted Answer

The maximum power output is determined by the Carnot efficiency, which is calculated using the temperatures of the heat source and sink. The Carnot efficiency is (1 - Tc/Th), where Tc is the cold reservoir temperature (4°C or 277K) and Th is the hot reservoir temperature (220°C or 493K). The efficiency is approximately 0.438, and the maximum power output is 0.438 * 420 kW = 183.96 kW, which rounds to 186 kW.

An Engineer Uses a River (Minimum Temperature of 4 ∘^{\circ}∘ C)to Cool His Electrical Plant Which Heats Water with a C)to

An Engineer Uses a River (Minimum Temperature of 4 $^{\circ}$ C)to Cool His Electrical Plant Which Heats Water with a C)to