My Math Forum Question regarding temperature inside a building

 Differential Equations Ordinary and Partial Differential Equations Math Forum

March 15th, 2015, 10:27 AM   #1
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From: Kent

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Question regarding temperature inside a building

I have spent 2 hours trying to answer this question to come to the conclusion that maybe not enough information is given in the question? Any help would be greatly appreciated. (Please see attachment).

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 March 15th, 2015, 11:09 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs I have deleted the second duplicate thread which was missing the attachment, and moved the original here. If the outside temperature is $M(t)$ and the inside temperature is $T(t)$, then by Newton's Law of Cooling, we may write the following IVP from the information given in the problem for part a): $\displaystyle \frac{dT}{dt}=k(-10-T)=-k(T+10)$ where $T(0)=20,\,T(1)=15$ The ODE in the IVP is separable. Can you first solve the ODE? Then we can use the given points on the temperature curve to determine the constant of integration and the constant $k$. Thanks from Mh430
March 15th, 2015, 01:00 PM   #3
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From: Kent

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Quote:
 Originally Posted by MarkFL I have deleted the second duplicate thread which was missing the attachment, and moved the original here. If the outside temperature is $M(t)$ and the inside temperature is $T(t)$, then by Newton's Law of Cooling, we may write the following IVP from the information given in the problem for part a): $\displaystyle \frac{dT}{dt}=k(-10-T)=-k(T+10)$ where $T(0)=20,\,T(1)=15$ The ODE in the IVP is separable. Can you first solve the ODE? Then we can use the given points on the temperature curve to determine the constant of integration and the constant $k$.
thank you Mark, Newtons law of cooling went straight over my head when trying to answer this question, i can now do this by myself, thank you and i woud be grateful if you could look at my other thread

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