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At 2:00 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 22° C in your house. At 9:00 pm, it is 12° C in the house, and you notice that it is -5° C outside. (a) Assuming that the temperature, T, in your home obeys Newton's Law of Cooling, write the differential equation satisfied by T. (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 estimate the temperature in the house when you get up at 6:00 am the next morning. Temperature = с + 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?) Revise ?

At 2:00 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 22° C in your house. At 9:00 pm, it is 12° C in the house, and you notice that it is -5° C outside. (a) Assuming that the temperature, T, in your home obeys Newton's Law of Cooling, write the differential equation satisfied by T. (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 estimate the temperature in the house when you get up at 6:00 am the next morning. Temperature = с + 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?) Revise ?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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At 2:00 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 22°C in your house. At 9:00 pm, it is 12° C in the house, and you notice that it is −5° C 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 6:00 am the next morning. Temperature = Should you worry about your water pipes freezing? ? C + (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?) Revise ? ♦
Transcribed Image Text:At 2:00 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 22°C in your house. At 9:00 pm, it is 12° C in the house, and you notice that it is −5° C 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 6:00 am the next morning. Temperature = Should you worry about your water pipes freezing? ? C + (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?) Revise ? ♦
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