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A = atmospheric temperature in kelvin; M = temperature difference produced by heat pump; CP is coefficient of performance; Th is the temperature of the hot sink; Tc is the temperature of the cold sink

Carnot: CP = Th/(Th-Tc)
th = A + M; tc = A - M

∴ CP = (A+M)/(A+M-A+M) = (A+M)/(2M)