Question

(i point) At 1:00 pm one winter afternoon, there is a power failure at your house in Wisconsin, and your heat does not work without electricity. When the power goes out, it is 70°F in your house. At 11:00 pm, it is 54°F in the house, and you notice that it is 6F outside. (a) Assuming that the temperature, T',in your home obeys Newton's Law of Cooling, write the differential equation satisfied by T. dT dt (Use k for any constant of proportionality in your equation; your equation may involve T and the values in the problem. (b) Solve the differential equation to estimate the temperature in the house when you get up at 8:00 am the next morning Temperature Should you worry about your water pipes freezing?? (c) Think about your equation in (a): what assumption did you make about the temperature outside? Given this (probably incorrect) assumption, would you revise your estimate up or down? (And why?) Revi up down Note: credit for this problem all answers must be correct.

Answer 1

eon uo coolng dT I T-TS Telegrahma㎝ both sides dT K七 Given Tg = 6 r to) K (10) and also T (o) 54 546+ 64 e job 48 64

Exercise No. LIL o, b) 8.00 Am the ne d moming t 64659 6t 31.05D9 43 05I °F 0.54 Cc) we anmuned o tempevathue outside be c6 uhich is a goess over simpriftadien Sinc uce woould expd the adisde tempto dvop behoen nM to AM, hod would maan the house cods te eirg H simptiffan od than ouon model, so 8 n wooold el be Wwes han 43 F

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