#### Question

Newton's law of cooling is a special case of

Wien's displacement law

Kirchhoff's law

Stefan's law

Planck's law

#### Solution

Stefan's law

From Stefan-Boltzman's law, the energy of the thermal radiation emitted per unit time by a blackbody of surface area *A* is given by, `u = σAT^4`

Where `σ` is Stefan's constant.

Suppose a body at temperature *T* is kept in a room at temperature *T*_{0}.

According to Stefan's law, energy of the thermal radiation emitted by the body per unit time is `u = eσAT^4`

Here, *e* is the emissivity of the body.

The energy absorbed per unit time by the body is (due to the radiation emitted by the walls of the room

`Δu = eσAT_0^4`

Thus, the net loss of thermal energy per unit time is

`Δu = eσA ( T^4 - T_0^4 )`

Newton law of cooling is given by

`(dT)/(dt) = -bA( T - T_0 )`

This can be obtained from equation (i) by considering the temperature difference to be small and doing the binomial expansion.