- #1
brusier
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Newton's Law of Cooling (diff eq. -- separation of variables)
Fresh coffee sitting in a room cooling...you know the routine.
Anyhow T(0) = 90degreesCelcius.
Room temp=25degrees celsius
find k.
Then he asks us to use Euler's method to estimate coffee temp after five mins. (using step size h=1).
T(t) satisfies the equation: dT/dt=k(T-Troom).
we know that at T=65 degrees (for coffee) dT/dt (or the rate of cooling, as the problem states)= 1 degree per minute
Well thought hey look here the ole plug and chug MAY work, let's see...:
1=k(65-25) brings k=.025. but then I thought, hey for the crap to cool k needs to be negative (this is the only way the limit as t tends to infinity for e^(kt) to tend to 0). So this can't be the appropriate way of going about this. So, without thinking (again) I integrated to see if that would bring about new light. I got
T=65e^(kt)+25.
No real help even if the integration is right because I'm missing a value for t to help me solve for k. So I'm a little stuck here.
I'm confused even more in that the blank where the answer to the second part goes, the Euler's method answer, has a blank that reads T(10)=____________. But I know (thought) the question asked for T(5). Am I missing somthing here?? Thank you, Ian.
Homework Statement
Fresh coffee sitting in a room cooling...you know the routine.
Anyhow T(0) = 90degreesCelcius.
Room temp=25degrees celsius
find k.
Then he asks us to use Euler's method to estimate coffee temp after five mins. (using step size h=1).
Homework Equations
T(t) satisfies the equation: dT/dt=k(T-Troom).
we know that at T=65 degrees (for coffee) dT/dt (or the rate of cooling, as the problem states)= 1 degree per minute
The Attempt at a Solution
Well thought hey look here the ole plug and chug MAY work, let's see...:
1=k(65-25) brings k=.025. but then I thought, hey for the crap to cool k needs to be negative (this is the only way the limit as t tends to infinity for e^(kt) to tend to 0). So this can't be the appropriate way of going about this. So, without thinking (again) I integrated to see if that would bring about new light. I got
T=65e^(kt)+25.
No real help even if the integration is right because I'm missing a value for t to help me solve for k. So I'm a little stuck here.
I'm confused even more in that the blank where the answer to the second part goes, the Euler's method answer, has a blank that reads T(10)=____________. But I know (thought) the question asked for T(5). Am I missing somthing here?? Thank you, Ian.