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PsiPhi
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Homework Statement
The time it takes for a deceased human body to reach room temperature.
Room temperature = 25 degrees C
Initial temperature of corpse = 37 degrees C
Homework Equations
I used Newton's law of cooling: [tex]\frac{dT}{dt} = -k(T - T_{room})[/tex]
where T is a function of t(time in seconds), T(room) is the room temperature and k is the experimental constant.
The Attempt at a Solution
Well the solution to the D.E was simple, it is [tex] T(t) = 12e^{-kt} + 25[/tex]
Ok, now I don't know enough information to determine k(the experimental constant). I generated various values of T(t) until it reach 25degreesC. For k = 1, it took 100secs to get to 25.(this seemed unreasonable). For k = 0.001, it took approximately 6 hrs(this seemed reasonable). Now for my problem is there way I can determine k, without resorting to plugging in random values of k. I was thinking of using the heat capacity of water to approximate the human, but then how is that related to k?
Thanks
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