Question

(a) A Carnot engine has a power output of 224 kW. The engine operates between two reservoirs at 21◦C and 484◦C. How much thermal energy is absorbed each hour?

Answer in units of J.

(b) How much thermal energy is lost per hour? Answer in units of J.

Answer 1

To calculate the thermal energy absorbed per hour, use the formula Q = P / efficiency. To calculate the thermal energy lost per hour, subtract the absorbed energy from the total energy input.

Step-by-step explanation:

A Carnot engine is a theoretical engine that operates between two reservoirs at different temperatures and is considered to be the most efficient engine possible. To calculate the thermal energy absorbed per hour, we can use the formula:

Q = P / efficiency = 224 kW / (1 - Tc/Th)

Where P is the power output, Tc is the temperature of the cold reservoir in Kelvin (21 + 273 = 294 K), and Th is the temperature of the hot reservoir in Kelvin (484 + 273 = 757 K). Plugging in the values, we get:

Q = 224,000 W / (1 - 294/757) = 224,000 W / 0.613 = 365,271.83 J/hour.

To calculate the thermal energy lost per hour, we need to subtract the absorbed energy from the total energy input:

Lost energy = Total energy - Absorbed energy = P - Q = 224 kW - 365,271.83 J/hour = -365,047.83 J/hour. (Negative value indicates energy loss)