Two uniform solid spheres made of copper have radii 15   cm and 20   cm respectively. Both of them are heated to a temperature of 70 ° C and then placed in a region of ambient temperature equal to 45 ° C . What will be the ratio of the initial rates of cooling of both the spheres?

Step-by-step solution

For two bodies made up of same material, rate of loss of heat will depend only on their surface area for same temperature change. ∴    d Q d t 1 d Q d t 2 = A 1 A 2 = r 1 2 r 2 2     … … i Ratio of initial rates of cooling = d θ d t 1 d θ d t 2 As, dQ dt = mc d θ dt ∴    m 1 c 1 ( d θ / dt ) 1 m 2 c 2 ( d θ / dt ) 2 = r 1 2 r 2 2 ...[from (i)] since, both the spheres are made up of copper, c 1 = c 2 = c . ∴    d θ d