Question

Two circular discs $A$ and $B$ with equal radii are blackened. They are heated to same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?

• A. A and B have same specific heats
• B. specific heat of A is less
• C. specific heat of B is less
• D. nothing can be said

Answer 1

Answer: (B)

When a body cools by radiation, the rate of cooling is given by
$\frac{d\theta}{dt}=-\frac{eA\sigma}{ms}\left(\theta^{4}-\theta_{0}^{4}\right)$
$-ve$ sign shows that temperature decreases i.e. the body cools where s is the specific heat of the material and $\theta_{0}$ is the surrounding temperature
or, $\frac{d\theta}{dt} \propto \frac{1}{s}$
i.e. rate o f cooling $(R=d\theta/dt)$ is inversely proportional to the specific heat of material. For A, rate o f cooling is large. Therefore specific heat of A is smaller.