Question

For a certain ideal Carnot engine, the hot reservoir is 35°C higher than the cold reservoir. If this engine is to have an efficiency of 20%, what must be the temperature of the hot reservoir?

Answer 1

To find the temperature of the hot reservoir for a Carnot engine with an efficiency of 20%, we can use the Carnot efficiency formula. The temperature of the hot reservoir is 43.75°C.

Step-by-step explanation:

To find the temperature of the hot reservoir, we need to use the Carnot efficiency formula:

Efficiency (η) = 1 - (Tc/Th)

where η is the efficiency, Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir.

Given that the efficiency is 20% (or 0.20) and the cold temperature is 35°C, we can rearrange the formula to solve for Th:

Th = Tc / (1 - η)

Substituting the values, we get:

Th = 35 / (1 - 0.20) = 35 / 0.80 = 43.75°C

Therefore, the temperature of the hot reservoir must be 43.75°C.