A home heat air standard pump is installed using the ambient

A home heat, air standard pump is installed using the ambient outdoor air as T_highReservoir. Try summer outdoor temperatures of 35 degree C, 40 degree C, and 45 degree C and estimate percent savings in electricity if the house is kept at 28 degree C instead of 22 degree C.

Solution

COP   = T_L / (T_H - T_L)

for T_L   = 22 C

COP1   = 273 + 22 / (35 - 22 )   = 22.692

COP1   = 273 + 22 / (40 - 22 )   = 16.4

COP1   = 273 + 22 / (45 - 22 )   = 12.826

for T_L   = 28 C

COP1   = 273 + 28 / (35 - 28 )   = 43

COP1   = 273 + 28 / (40 - 28 )   = 25.083

COP1   = 273 + 28 / (45 - 28 )   = 17.7

% savings 1 = 43 - 22.692 / 22.692   = 89.49 %

% savings 2 = 25.083 -16.4 / 16.4   = 52.94 %

% savings 3 = 17.7 - 12.826 /12.826   = 38 %