According to Stefan’s law of radiation, the absolute temperature T of a body cooling in a medium at constant temperature Tm 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 compared to Tm then Newton’s law of cooling approximates Stefan’s law. [Hint: Think binomial series of the right-hand side of the DE.]
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