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Math Help - Linear Models

  1. #1
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    Linear Models

    how many hours elapsed when the body was found...

    That is link to the previous problem posted by another student.

    My question is:

    The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification is:


    where k<0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 150 degree F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 100 degree F. If Tm = 70 degree F, then what is the temperature of the coffee cup B after 30 min?

    help is greatly appreciated!
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  2. #2
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    Re: Linear Models

    Quote Originally Posted by leonhart View Post
    how many hours elapsed when the body was found...

    That is link to the previous problem posted by another student.

    My question is:

    The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification is:


    where k<0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 150 degree F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 100 degree F. If Tm = 70 degree F, then what is the temperature of the coffee cup B after 30 min?

    help is greatly appreciated!
    Separate variables:

    \frac{dT}{T-T_m}=kSdt

    Now integrate both sides of the equation.
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