First slide

Radiation

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 your draw from their cooling curves?

Moderate

A

A and B have same specific heat
B

Specific heat of A is less
C

Specific heat of B is less
D

Nothing can be said

Solution

When a body cools by radiation, the rate of cooling is given by:
$\frac{dθ}{dt} = - \frac{eAσ}{ms} (θ^{4} - {θ^{4}}_{0})$
-ve sign shows that temperafure decreases, i.e., the body cools, s is the specific heat of material and $θ_{0}$ is the surrounding temperature
or $\frac{dθ}{dt} \propto \frac{1}{s}$
i.e., rate of cooling(R = $\frac{dθ}{dt}$ ) is inversely proportional to the specific heat of material. For a, rate of cooling is large, therefore, specific heat of A is smaller.

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