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Math Help - Newton's Law of Cooling Derivation

  1. #1
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    Wink Newton's Law of Cooling Derivation

    x(t) = Temperature of an object at time t.
    (k < 0)
    T = surrounding cooler temperature.

    Given:
    (dx/dt) = k(x(t) - T)

    Derive using differential equations and show it equals:
    x(t) = T + Ce^kt
    Where C is a constant.


    Attempt:
    dx = k(x(t) - T) dt

    Then integrate both sides?
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  2. #2
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    Re: Newton's Law of Cooling Derivation

    If you are trying to separate the variables then pull x(t) onto the LHS with dx.
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  3. #3
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    Re: Newton's Law of Cooling Derivation

    You cannot integrate x(t) with respect to t because you do not yet know what specific function of t x is.
    As Chi Sigma says, you can "pull x(t) onto the LHS with dx" and integrate
    \int \frac{dx}{x- T}= \int dt

    Note that T is a constant.
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  4. #4
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    Re: Newton's Law of Cooling Derivation

    Quote Originally Posted by HallsofIvy View Post
    As Chi Sigma says,
    I wish I was that good with D.E.s! ;-)
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