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.