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 $(W = 1 J)$
$Q_1 = \frac{t_1 +273}{t_1 -t_2}$