The coefficient of performance (β) of a refrigerator is given by β=WQ2=T1−T2T2, where Q2 is the heat extracted from the refrigerator (cold reservoir), W is the work done (electrical energy consumed), T1 is the absolute temperature of the room (hot reservoir), and T2 is the absolute temperature inside the refrigerator.
The total heat delivered to the room is Q1=Q2+W.
We need to find the amount of heat delivered per joule of work done, which is WQ1.
WQ1=WQ2+W=WQ2+1=β+1
Substituting the expression for β:
WQ1=T1−T2T2+1=T1−T2T2+T1−T2=T1−T2T1
Converting the given Celsius temperatures to Kelvin:
T1=t1+273
T2=t2+273
Now, substitute the temperatures into the ratio:
WQ1=(t1+273)−(t2+273)t1+273=t1−t2t1+273
For each joule of electrical energy consumed (W=1 J), the heat delivered is t1−t2t1+273.