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 is related to the temperature di erence by a linear relation,
Q = A[T1 T2] ;
where A is a constant. Derive an experssion for T2 in terms of T1, E, and A for continuous operation when the steady state has been reached.