According to Stefan’s law of radiation the absolute temperature T of a body cooling in a...

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

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 − Tm is small in comparison to T_m then Newton’s law of cooling approximates Stefan’s law. [Hint: Think binomial series of the right-hand side of the DE.]