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Math Help - Newton's law of cooling

  1. #1
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    Newton's law of cooling

    I was looking over a past exam paper today and came across this longer question. I'm unsure of which values to use, and where to go once I find these values.

    A murder victim has been shot through the head with a revolver. A suspect is found standing over the victim at 10:15PM holding the revolver. At 10:30PM, the coroner records a body temperature of 26C and it was also recorded that the room temperature was 21C. An hour later a second reading of the body temperature yielded 24C. The suspect was seen in public from 6PM to 9PM. Given that the normal body temperature of a living person is 37C, use Newton’s law of cooling to determine whether or not the suspect has an alibi.


    Thanks
    Last edited by Danog; October 25th 2009 at 03:18 AM.
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  2. #2
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    With Newton's Law of Cooling, you can either remember the formula or remember the idea behind it and derive it. It is kind of a pain to derive under pressure if you haven't done it a few times, so maybe you should just memorize it when you have to use it.

    The end result is: T(t) = T_a+(T_0-T_a)e^{-kt}

    You are given T_0 and T_a, the starting temp for the body and the ambient, or outside temperature. The only thing left to find is k, the decay rate. Since you are given information about the temperature after a certain time, t, you can plug everything in except for the missing k. Solve for k.
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  3. #3
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    Would t be in minutes or hours? It doesn't say in the question which one to use.
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  4. #4
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    Quote Originally Posted by Danog View Post
    Would t be in minutes or hours? It doesn't say in the question which one to use.
    Either one will work as long as you are consistent. I would use hours.
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  5. #5
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    Wait... Would you start taking t values from 10:15? That wouldn't give the suspect an alibi. I'm confused.
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  6. #6
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    Quote Originally Posted by Danog View Post
    Wait... Would you start taking t values from 10:15? That wouldn't give the suspect an alibi. I'm confused.
    No. The first temperature reading for the body was at 10:30. Then the next one was an hour later. What is not making sense? I want to help but need you to be more explicit.
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