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
(a) T2 − T1
(b) T22 - T21
(c) T32 - T31
(d) T42 - T41

Answer 1

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  T42 - T41

Explanation:

• $\mathrm{T}_{2}^{4}-\mathrm{T}_{1}^{4}$ The thermal radiation energy released per unit time by a black body of surface area A is given by Stefan-Boltzmann law.

• $u=\sigma A T^{4}$

• Stefan-Boltzmann is constant here.

• Because the solid's temperature is lower than the surroundings, the solid's temperature will rise with time until it reaches a balance with the surroundings. The solid emission rate is proportional to $T_{1}^{4}$ and the surrounding emission rate is proportional to $T_{2}^{4}$ .

• The net temperature rise rate will therefore be proportional to $\mathrm{T}_{2}^{4}-\mathrm{T}_{1}^{4}$.