An electrical generating plant operates at a boiler temperature of 224°C and exhausts the unused heat into a nearby river at 21°C.What is the maximum theoretical efficiency of the plant? (0°C = 273 K)

A) 17%
B) 7%
C) 64%
D) 41%
E) 74%

Question

An electrical generating plant operates at a boiler temperature of 224°C and exhausts the unused heat into a nearby river at 21°C.What is the maximum theoretical efficiency of the plant? (0°C = 273 K)
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A) 17%
B) 7%
C) 64%
D) 41%
E) ​74%

Quizplus · Accepted Answer

The maximum theoretical efficiency of a heat engine is given by the Carnot efficiency formula: η = 1 - (Tc/Th), where Tc and Th are the absolute temperatures of the cold and hot reservoirs, respectively. Converting the given temperatures to Kelvin: Th = 224°C + 273 = 497 K and Tc = 21°C + 273 = 294 K. Thus, η = 1 - (294/497) ≈ 0.409 or 41%.

An Electrical Generating Plant Operates at a Boiler Temperature of 224°C