An ideal air conditioner operating on a Carnot cycle absorbs heat Q2 from a house at temperature T2 and discharges Q1 to the outside at temperature T1, consuming electrical energy E. Heat leakage into the house follows Newton's law,
Q=A[T1−T2],(13.42)
where A is a constant. Derive an expression for T2 in terms of T1, E, and A for continuous operation when the steady state has been reached.
The air conditioner is controlled by a thermostat. The system is designed so that with the thermostat set at 20∘C and outside temperature 30∘C the system operates at 30\% of the maximum electrical energy input. Find the highest outside temperature for which the house may be maintained inside at 20∘C.