Newton's Law of Cooling ?

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Newton's Law of Cooling ?

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Answer 1 · 2016-11-18T13:28:50

$T(t) = 3/k(kt+e^(-kt)-1)$

Explanation:

Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between the ambient temperature and its own temperature.

$d/dt T(t) =k(3t -T(t))$ or

$d/dt T(t) +k T(t) =3kt$

Here $k$ is the proportionality constant.

Solving this differential equation we have

$T(t)=(3(k t-1))/k+C_1 e^(-k t)$

Applying the initial conditions we have

$T(0) = 0$ so $-3/k+C_1=0$ then

$T(t) = 3/k(kt+e^(-kt)-1)$

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Newton's Law of Cooling ?

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Explanation:

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