An electrical generating plant operates at a boiler temperature of 218°C and exhausts the unused heat into a nearby river at 24°C.What is the maximum theoretical efficiency of the plant? (0°C = 273 K)
A)16%
B)62%
C)63%
D)40%
E)73%

Question

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 = 218°C + 273 = 491 K, Tc = 24°C + 273 = 297 K. Thus, η = 1 - (297/491) ≈ 0.395 or 39.5%, which rounds to 40%.

An Electrical Generating Plant Operates at a Boiler Temperature of 218°C