22. 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 - T₂2] 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. ​