A heat engine that operates on a Carnot cycle has efficiency \(\eta\). When the engine is run in reverse as a heat pump, what are, in terms of \(\eta\) 

(a) the coefficient of performance of cooling when the pump is used for cooling and 

(b) the coefficient of performance of heating when the pump is used for heating?

(c) For each case, check your answer to see whether the range of the coefficients of performance is physically reasonable.