A solid at temperature T1 is kept in an evacuated chamber at temperature T2 T1. The rate of increase of temperature of the body is proportional to

Question

A solid at temperature T1 is kept in an evacuated chamber at temperature T2 > T1. The rate of increase of temperature of the body is proportional to

KollegeApply · Accepted Answer

T_2^4 - T_1^4 From Stefan-Boltzmann law, the energy of thermal radiation emitted per unit time by a blackbody of surface area A is given by u = σAT^4 Here, σσ is Stefan-Boltzmann constant. Since the temperature of the solid is less than the surroundings, the temperature of the solid will increase with time until it reaches equilibrium with the surroundings. The rate of emission from the solid will be proportional to T_1^4 and rate of emission from the surroundings will be proportional to T_2^4. So, the net rate of increase in temperature will be proportional to T_2^4 - T_1^4.

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