Question
A solid sphere of copper of radius R and a hollow sphere of the same material of inner radius r and outer radius R are heated to the same temperature and allowed to cool in the same environment. Which of them starts cooling faster? Explain your answer.
Solution
In this case, the external radius of both the spheres is same.
The surface areas area of both spheres are same.
If the two spheres are heated to the same temperature and allowed to cool in the same environment, then the rate of loss of heat dQ/dt of both the spheres is same.
Therefore the rate of cooling dT/dt is inversely proportional to mass of the sphere.
The mass of the hollow sphere is less than that of solid sphere. Therefore, the rate of cooling of hollow sphere is faster than that of solid sphere.
