A household refrigerator operates with cold- and hot-temperature reservoirs of T_c = 5°C and T_h = 25°C, respectively. When new, the cold and hot side resistances are R_c,n = 0.05 K/W and R_h,n = 0.04 K/W, respectively. Over time, dust accumulates on the refrigerator’s condenser coil, which is located behind the refrigerator, increasing the hot side resistance to R_h,d 0.1 K/W. It is desired to have a refrigerator cooling rate of q_in = 750 W. Using the results of Problem 1.38, determine the modified coefficient of performance and the required power input W under 

(a) Clean and 

(b) Dusty coil conditions.

Data From Problem 1.38

An internally reversible refrigerator has a modified coefficient of performance accounting for realistic heat transfer processes of

where q_in is the refrigerator cooling rate, q_out is the heat rejection rate, an W is the power input. Show that COPm can be expressed in terms of the reservoir temperatures T_c and T_h, the cold and hot thermal resistances R_t,c and R_t,h, and q_in, as

where R_tot = R_t,c + R_t,h. Also, show that the power input may be expressed as

Transcribed Image Text:

COP Ti 9in W lout Gin Thị T