Question

please solve and show work and have neat handwriting because it is mandatory for the neatness

According to Stefan's law of radiation the absolute temperature T of a body cooling in a medium at constant absolute temperature 7 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) Solive the differential equation approximates Stefan's law. (Hint: Think binomial series of the right-hand side of the DE.] (o) Show that when - Im is smal In comparison to Tm then Newton's low of cooling Using the binomial s series, we expand the right side of the previous equation. (Enter the frst three terms of the expansion.) dT can be ignored, giving d: ki(T-Tm), where ki-4kr", When T- Tm is smail compared to Tm Sele

Answer 1

TT-Tm T- T 2 2. 2 2 2. 0只 2. 2 2. 2- הל

2 2. 0 90 2. Tm 2 when Can be ighoned dst 3