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Two circular discs $A$ and $B$ with equal radii are blackend. They are heated to same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves ?
$A$ and $B$ have same specific heats
Specific heat of $A$ is less
Specific heat of $B$ is less
Nothing can be said
Solution
When a body cools by radiation, the rate of cooling is given by $:$
$\frac{\mathrm{d} \theta}{\mathrm{dt}}=-\frac{\mathrm{eA} \sigma}{\mathrm{ms}}\left(\theta^{4}-\theta_{0}^{4}\right)$
$-$ve sign shows that temperature decreases, i.e.,
the body cools. $s$ is the specific heat of material and $\theta_{0}$ is the surrounding temperature
$\mathrm{Or}$ $\mathrm{d} \theta / \mathrm{dt} \propto 1 / \mathrm{s}$
i.e., rate of cooling $(\mathrm{R}=\mathrm{d} \theta / \mathrm{dt})$ is inversely proportional to the specific heat of material. For $A,$ rate of coolling is large, therefore, specific heat of $\mathrm{A}$ is smaller.
