Question

Newton's Law of Cooling ?

Answer 1

`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)`