Question

A Carnot engine is operated between two heat reservoirs at temperatures of 520 K and 300 K. If the engine receives 6.45 kJ of heat energy from the reservoir at 520 K in each cycle, how many joules per cycle does it reject to the reservoir at 300 K?

Answer 1

The Carnot engine rejects 2.73 kJ of heat to the reservoir at 300 K.

Step-by-step explanation:

A Carnot engine operates between two heat reservoirs at temperatures of 520 K and 300 K. The engine receives 6.45 kJ of heat energy from the reservoir at 520 K in each cycle. To find the amount of heat rejected to the reservoir at 300 K, we can use the formula for the efficiency of a Carnot engine:

Efficiency (ε) = 1 - (Temperature of the reservoir at 300 K / Temperature of the reservoir at 520 K)

Using the given temperatures, the efficiency of the Carnot engine is 1 - (300 / 520) = 0.423. Since the engine receives 6.45 kJ of heat from the 520 K reservoir, the amount of heat rejected to the 300 K reservoir can be calculated as:

Heat rejected = Efficiency * Heat received = 0.423 * 6.45 kJ = 2.73 kJ