Question

A Carnot engine has a power output of 163 kW. The engine operates between two reservoirs at 31◦C and 469◦C.
1. How much thermal energy is absorbed each hour? Answer in units of J.
2. How much thermal energy is lost per hour? Answer in units of J.

Answer 1

Temperature of reservoirs:

$$T_C=31^\circ C = 304 K,\, T_H=469^\circ C = 742 K$$

1 hour equals to 3600 seconds.

Efficiency:

$$\eta = \frac{W}{Q_H}=\frac{T_H - T_C}{T_H}=0.5903$$

Therefore, thermal energy consumption:

$$Q_H= W \frac{T_H}{T_H - T_C} = 276\, kW$$

thermal energy loss:

$$Q_C=Q_H-W= W \frac{T_C}{T_H - T_C} = 113\, kW$$

1. Thermal energy is absorbed each hour:

$$276\, kW \cdot 3600 \, s = 994077 \, J$$

2. Thermal energy is lost per hour:

$$113\, kW \cdot 3600 \, s =407277 \, J$$