A residential heat pump operates by extracting thermal energy \(Q_C\) from cold outdoor air at temperature \(T_C\) and delivering thermal energy \(Q_H\) to the warm interior of a house at temperature \(T_H\). To accomplish this transfer, an electric compressor performs work \(W\) on the working fluid during each cycle. Which of the following correctly compares \(Q_H\) to \(W\) and provides the correct thermodynamic justification?