question_answer

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?         

Answer:

                 Rate of loss of heat by any sphere,                 \[m\times c\times \left( -\frac{dT}{dt} \right)=\sigma A({{T}^{4}}-T_{0}^{4})\] Now \[\sigma ,A,({{T}^{4}}-T_{0}^{4})\] are same for both the spheres, so the rate of cooling, \[-\frac{dT}{dt}\propto \frac{1}{m}\] Since the hollow sphere has less mass, its rate of cooling will be faster.