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Math Help - Newton's law of cooling.

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    Newton's law of cooling.

    Hi Everyone, can someone please help me with this? It has to do with Newton's Law of cooling.

    A fast food resturant wants a container that can quickly cool coffee from 200 degrees to 130 degrees and keep the liquid between 110 and 130 degrees for as long as possible. Here are the choices:
    a. CK company has a containter that reduces the temp of a liquid from 200 degrees to 100 degrees in 30 mins by maintaining a constant temp of 70.

    b. Temp company has a container that reduces the temp of a liquid from 200 to 110 degrees in 25 mins by maintaining a constant temp of 60 degrees.

    Use Newton's law of cooling to find a function relating the temp of the liquid over time for each container.
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    Quote Originally Posted by jkeo789 View Post
    Hi Everyone, can someone please help me with this? It has to do with Newton's Law of cooling.

    A fast food resturant wants a container that can quickly cool coffee from 200 degrees to 130 degrees and keep the liquid between 110 and 130 degrees for as long as possible. Here are the choices:
    a. CK company has a containter that reduces the temp of a liquid from 200 degrees to 100 degrees in 30 mins by maintaining a constant temp of 70.

    b. Temp company has a container that reduces the temp of a liquid from 200 to 110 degrees in 25 mins by maintaining a constant temp of 60 degrees.

    Use Newton's law of cooling to find a function relating the temp of the liquid over time for each container.
    Newton's law of cooling says that heat flows from a hotter body to a cooler body at a rate proportional to the difference between the temperatures of the two bodies. That is:
    \frac{dT}{dt}= T- c
    where "T" is the temperature of the coffee, "t" is the time of cooling and c is the temperature of the container.

    For a) you have \frac{dT}{dt}= k(T- 70). Integrating that will give a "constant of integration" as well as the "constant of proportion", k. To find both of those constants, use the fact that T(0)= 200 and T(30)= 100.

    For b) you have \frac{dT}{dt}= k(T- 60). Integrating that will give a "constant of integration" as well as the "constant of proportion", k. To find both of those constants, use the fact that T(0)= 200 and T(25)= 110.
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