According to Stefan’s law of radiation the absolute temperature T of a body cooling in a medium at constant absolute temperature Tm is given by

dT/dt = k(T⁴ - T⁴_m),

where k is a constant. Stefan’s law can be used over a greater temperature range than Newton’s law of cooling.

(a) Solve the differential equation.

(b) Show that when T - T_m is small in comparison to Tm then Newton’s law of cooling approximates Stefan’s law.