Q143 / 160 · WBJEE 2015 · Physics

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

  • A
    $t_{2}^{4}-t_{1}^{4}$
  • B
    $\left(f_{2}^{4}+273\right)-\left(t_{1}^{4}+273\right)$
  • Correct answer
    C
    $t_{2}-t_{1}$
  • D
    $t_{2}^{2}-t_{1}^{2}$

Solution

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 $\Rightarrow \quad \frac{d \theta}{d t} \propto \theta-\theta_{0}$ Also $-\frac{d T}{d t} \propto T-T_{0}$ where, $T=$ temperature and $\quad t=$ time So, the rate of heat absorbed by cooled body is proportional to $t_{2}-t_{1}$

Hence, the correct answer is option: 'C'.

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