Reference no: EM131172026

An advertisement is noted in a rural newspaper for a dairy-barn unit that combines a milk cooler with a water heater. Milk must, of course, be refrigerated, and hot water is required for washing purposes. The usual barn is equipped with a conventional air-cooled electric refrigerator and an electric-resistance water heater. The new unit is said to provide both the necessary refrigeration and the required hot water at a cost for electricity about the same as the cost of running just the refrigerator in the usual installation. To assess this claim, compare two refrigeration units: The advertised unit takes 14.65 kW from a milk cooler at 272.15 K (-l0C), and discards heat through a condenser at 338.15 K (66°C) to raise the temperature of water from 286.15 K (13°C) to 336.15 K (63°C). The conventional unit takes the same amount of heat from the same milk cooler at 272.15 K (- 1 "C) and discards heat through an air-cooled condenser at 322.15 K (49°C); in addition, the same amount of water is heated electrically from 286.15 K (13°C) to 336.15 K (63°C). Estimate the total electric power requirements for the two cases, assuming that the actual work in both is 50% greater than required by Carnot refrigerators operating between the given temperatures.