Question

Which of the laws can be understood in terms of Stefan’s law?
A. Wien’s displacement law
B. Kirchoff’s law
C. Newton’s law of cooling
D. Planck’s law

Answer 1

The law that can be understood in terms of Stefan’s law, is the rate of cooling of an object is related to the temperature differential between the object and its surroundings, where a body that is exposed, changes the temperature via radiation is approximately proportional to the difference between the object's temperature and its surroundings, and the provided difference is low.

Complete step by step answer:
Because Newton's law of cooling is an approximate version of Stefan's law, it can be interpreted in terms of Stefan's law.According to Stefan's law:
$\text{Rate of cooling} = \dfrac{{dT}}{{dt}} = \dfrac{{eA\sigma }}{{mC}}({T^4} - T_0^4)$
where, $T$ is the temperature of the body and ${T_0}$ is the temperature of the surroundings.

Newton’s law of cooling:
${T^4} - T_0^4\propto \Delta T$
According to Newton's law of cooling, the rate of heat loss of a body is directly proportional to the temperature differential between the body and its surroundings. The law is typically qualified by the requirement that the temperature difference be modest and that the nature of the heat transfer mechanism remain unchanged. As a result, it's the same as saying the heat transfer coefficient, which mediates heat losses and temperature changes, is constant.

Because the thermal conductivity of most materials is only slightly dependent on temperature, this requirement is generally met in heat conduction (where it is guaranteed by Fourier's law). Newton's Law is obeyed for forced air or pumped fluid cooling when the fluid parameters do not change greatly with temperature, but it is only fundamentally true for buoyancy-driven convection, when the flow velocity increases with temperature difference.Finally, Newton's law of cooling only applies to very tiny temperature changes in the case of heat transfer by thermal radiation.

Hence, the correct option is (C).

Note: Stefan's law expresses the total power per unit surface area (also known as intensity) radiated by an object, which is commonly assumed to be a blackbody. Wien's Law is the formula used to calculate what wavelength the power peaks at.