Question

A solid maintained at $t_{1}^{\circ} C$ is kept in an evacuated chamber at temperature $t_{2}^{\circ} C$ $\left(t_{2} \gg t_{1}\right)$. The rate of heat absorbed by the body is proportional to

• A. $t_{2}^{4} - t^{4}_{1} $
• B. $\left(t_{2}^{4} +273\right) - \left(t^{4}_{1} +273\right)$
• C. $t_{2} - t_{1}$
• D. $t_{2}^{2} - t_{1}^{2}$

Answer 1

Answer: (C)

As we know that, the rate of cooling is
$\frac{d \theta}{d t}=b A\left(\theta-\theta_{0}\right)$
where, $b A=$ constant
$\Rightarrow \frac{d \theta}{d t} \propto \theta-\theta_{0}$
Also $-\frac{d T}{d t} \propto T-T_{0}$
where, $T=$ temperature
and $t=$ time
So, the rate of heat absorbed by cooled body is proportional to $t_{2}-t_{1}$.