According to Stefan's law of radiation the absolute temperature T of a body cooling in a medium at constant absolute temperature is given by - 4(7¹-7¹). de where 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 4T M+Cx (b) Show that when 7-T is small in comparison to T, then Newton's law of cooling approximates Stefan's law. (Hint: Think binomial series of the right-hand side of the DE.) OT - 4(74-72) of . Using the binomial series, we expand the right side of the previous equation. (Enter the first three terms of the expansion.) . When 7-T is small compared to T- can be ignored, giving(7-7), where ₁-47

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