Page 1 PROBLEM 3.1 KNOWN: One-dimensional, plane wall ...

PROBLEM 3.16KNOWN: Conditions associated with maintaining heated and cooled conditions within a refrigeratorcompartment.FIND: Coefficient of performance (COP).SCHEMATIC:ASSUMPTIONS: (1) Steady-state operating conditions, (2) Negligible radiation, (3) Compartmentcompletely sealed from ambient air.ANALYSIS: The Case (a) experiment is performed to determine the overall thermal resistance to heattransfer between the interior of the refrigerator and the ambient air. Applying an energy balance to acontrol surface about the refrigerator, it follows from Eq. 1.11a that, at any instant,E g − E out = 0Hence,q elec − q out = 0where qout = ( T∞,i − T∞,o ) Rt. It follows that( − )$T∞,i − T∞,o90 25 C$Rt= = = 3.25 C/Wqelec20WFor Case (b), heat transfer from the ambient air to the compartment (the heat load) is balanced by heattransfer to the refrigerant (q in = q out ). Hence, the thermal energy transferred from the refrigerator over the12 hour period isT∞,i − T∞,oQout = qout∆ t = qin∆ t = ∆tRt( − )$25 5 CQout= ( 12 h × 3600s h)= 266,000 J$3.25 C WThe coefficient of performance (COP) is thereforeQout266,000COP = = = 2.13