The temperature inside a refrigerator is `t_2^@C` and the room temperature is `t_1^@C`. The amount of heat delivered to the room for each joule of electrical energy consume ideally will be _____

Options

A. `(t_2+273)/(t_1-t_2)`
B. `(t_1+t_2)/(t_2+273)`
C. `(t_1)/(t_1-t_2)`
D. `(t_1+273)/(t_1-t_2)`

Answer

D

Explanation

Coefficient of performance of a refrigerator , `alpha =Q^2/W`
Heat released in reservoir `Q_1=W+Q_2`
`therefore Q_2=Q_1-W`
`therefore alpha=(Q_1-W)/W=Q_1/W-1`
`therefore Q_1/W=alpha+1`
but `alpha=(t_2+273)/(t_1-t_2)`
`therefore Q_1/W=(t_2+273)/(t_1-t_2)+1`
`=(t_2+273+t_1-t_2)/(t_1-t_2)`
`therefore Q_1/W=(t_1+273)/(t_1-t_2)`