What is the intake temperature of a Carnot heat engine with an exhaust temperature of 573 K and an efficiency of 30%?

To determine the intake temperature of a Carnot heat engine, you can use the relationship between efficiency, the temperatures of the hot and cold reservoirs. The formula for the efficiency (η) of a Carnot engine is given by:

η = 1 - (Tc/Th)

Where η is the efficiency, Tc is the absolute temperature of the cold reservoir (the exhaust temperature), and Th is the absolute temperature of the hot reservoir (the intake temperature).

In this scenario, the given efficiency is 30% (or 0.30 when expressed as a decimal), and the exhaust temperature Tc is 573 K. We can rearrange the equation to solve for Th:

0.30 = 1 - (573 K / Th)

Rearranging gives:

573 K / Th = 1 - 0.30

573 K / Th = 0.70

To isolate Th, we take the reciprocal:

Th = 573 K / 0.70

Now, calculating the above gives:

Th ≈ 819 K

This value indicates the temperature at which heat is being absorbed by the Carnot heat engine, confirming that the intake temperature is approximately 819 K. This reasoning shows that the Carnot engine operates with