Question

Two spheres of radii r1 and r2 have densities p1 and p2 and specific heats c1 and c2. if they are heated at same temperature the ratio of their rates of cooling will be

Answer 1

Hello friend,

● Answer-

(dθ1/dt)(dθ2/dt) = r2.p2.c2 / r1.p1.c1

◆ Explanation-

Here, rate of emission of radiation is same.

Q1 / A1dt = Q2 / A2dt

But we know, A = 4πr^2
Q = mcθ = (4/3πr^3)pcθ

(4/3πr1^3)p1c1dθ1 / 4πr1^2dt = (4/3πr2^3)p2c2dθ2 / 4πr2^2dt

Solving this, we'll get-

(dθ1/dt)(dθ2/dt) = r2.p2.c2 / r1.p1.c1

Hope this helps...