Question

An indoor heater operating on the Carnot cycle is warming the house up at a rate of 30 kJ/s to maintain the indoor temperature at 72 ºF. What is the power operating the heater if the outdoor temperature is 30 ºF?

Answer 1

$T_2 = 30\; °F = 272.039\; K$

Efficiency of heater $= 1- \frac{T_2}{T_1} = 1- (\frac{272.039}{295.372}) = 0.0789953$

The power operating the heater $= \frac{30 \; kJ/s }{ 0.0789953}$

$= 379.77 \; kJ/s \\ = 380 \; kJ/s$