According to Stefans law of radiation, the absolute temperature T of a body cooling in a
Chapter 2, Problem 36(choose chapter or problem)
According to Stefan’s law of radiation, the absolute temperature T of a body cooling in a medium at constant temperature \(T_{m}\) is given by
\(\frac{d T}{d t}=k\left(T^{4}-T_{m}^{4}\right)\),
(a) Solve the differential equation.
(b) Show that when \(T-T_{m}\) is small compared 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.]
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