Newton's Law of Cooling ?

1 Answer
Nov 18, 2016

Answer:

#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)#