If it is to be 40 percent efficient, a heat engine that exhausts heat at 350 K must absorb heat at a minimum temperature of
A) 210 K.
B) 583 K.
C) 875 K.
D) 1038 K.

Question

Quizplus · Accepted Answer

The maximum theoretical efficiency of a heat engine is given by (Th - Tc)/Th, where Th is the absolute temperature of the hot reservoir and Tc is the absolute temperature of the cold reservoir. If the engine is to be 40% efficient, then its maximum theoretical efficiency is 0.4, so we can write:

0.4 = (Th - Tc)/Th

Simplifying this equation, we get:

Th - Tc = 0.4 Th
0.6 Th = Tc

We are given that Tc = 350 K, so we can substitute this value to find Th:

Th = 0.6 Tc
Th = 0.6 x 350 K
Th = 210 K

Therefore, the minimum temperature at which the engine must absorb heat is 210 K, which corresponds to answer choice A (210 K = -63°C). However, this is the minimum temperature required for any heat engine to be 40% efficient, and it is not unique to this particular engine. Therefore, we cannot choose answer choice A as the best choice. Answer choice B is the best choice because it is the only temperature listed that is higher than Th, which means that it is the only temperature that would provide an efficiency of 40% or greater.

If It Is to Be 40 Percent Efficient, a Heat