8 An internally reversible refrigerator has a modified coefficient of performance accounting for realistic heat transfer processes of where qin is the refrigerator cooling rate, qout is the heat rejection rate, and is the power input. Show that COPm can be expressed in terms of the reservoir temperatures Tc and Th, the cold and hot thermal resistances Rt, c and Rt, h, and qin, as where Rtot Rt, c Rt, h. Also, show that the power input may be expressed as

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.