JEE Main 2014 Physics question
A black coloured solid sphere of radius R and mass M is inside a cavity with a vacuum inside. The walls of the cavity are maintained at temperature . The initial temperature of the sphere is . If the specific heat of the material of the sphere varies as per unit mass with the temperature T of the sphere, where α is a constant, then the time taken for the sphere to cool down to temperature will be (σ is Stefan Boltzmann constant)
Answer: (2)
Solution
Energy balance: . Putting so that , we get . Integrating from
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