42. You can prove in the following way that it is overall more
efficient for an
engine to exhaust at the ambient environmental temperature
than to exhaust
at a cooler temperature that requires refrigeration. Suppose
that the hot
reservoir is at Th, the ambient temperature is Ta, and the
refrigerated tem-
perature is Tc. The engine cannot put out more work than would
a Carnot
engine operating between Th and Tc, so Weng = eQh = a[(Th −
Tc)/Th] Qh,...