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

Stefan- Boltzmann Law is used.
According to the law, the energy of thermal radiation emitted per unit time by a body having surface area A is given as:

Here, e is the emissivity of the body and σ is the Stefan-Boltzmann constant and T is the Temperature.
As , temperature of solid will increase.
Now, for the solid the energy of thermal radiation is:

Energy of the thermal radiation in evacuated chamber is:

Now, the net difference in energy is .
Hence the net energy difference is proportional to:

Hence, The rate of increase of temperature of the body is proportional to .
For options (a), (b) and (c) the power od temperature difference is not 4. Hence, they are incorrect.
Thus, option (d) is the correct option.