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?

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? (A) A and B specific heat (B) Specific heat of A is less (C) Specific heat of B is less (D) Nothing can be said

Tardigrade Admin · Accepted Answer

When a body cools by radiation, the rate of cooling is given by:

\frac{d θ}{d t} = - \frac{e A σ}{m s} (θ^{4} - θ_{0}^{4})

-ve sign shows that temperature decreases, i.e., the body cools,

s

is the specific heat of material and

θ_{0}

is the surrounding temperature
or

\frac{d θ}{d t} \propto \frac{1}{s}

i.e., rate of cooling

(R = d θ / d t)

is inversely proportional to the specific heat of material. For a, rate of cooling is large, therefore, specific heat of

A

is smaller.

Q. 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?

A and B specific heat

Specific heat of A is less

Specific heat of B is less

Nothing can be said

Q. 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?