Question

The temperature inside a refrigerator is $t_2^{\circ }C$ and the room temperature is $t_1^{\circ }C$. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be

• A. $\frac{t_1}{t_1-t_2}$
• B. $\frac{t_1+273}{t_1-t_2}$
• C. $\frac{t_2+273}{t_1-t_2}$
• D. $\frac{t_1+t_2}{t_1-t_2}$

Answer 1

Answer: (B)

Temperature inside refrigerator $=t_2{}^{\circ }C$
Room temperature $t_1={}^{\circ }C$
For refrigerator,
$\frac{\text{Heat given to high temperature}\left(Q_1\right)}{\text{Heat taken from lower temperature}\left(Q_2\right)}=\frac{T_1}{T_2}$
$\frac{Q_1}{Q_2}=\frac{t_1+273}{t_2+273}$
$\Rightarrow \frac{Q_1}{Q_1-W}=\frac{t_1+273}{t_2+273}$
or $1-\frac{W}{Q_1}=\frac{t_2+273}{t_1+273}$
or $\frac{W}{Q_1}=\frac{t_1-t_2}{t_1+273}$
The amount of heat delivered to the room for each joule of electrical energy $(W=1J)$
$Q_1=\frac{t_1+273}{t_1-t_2}$