# Newton's law off cooling

## Homework Statement

First a glass of milk is put outside the refidgerator to heat, and its temperature changes from 6 degrees C to 13 C after two hours. When the temperature of the milk is 15 C the glass is put inside a refridgerator.
the problem is to find the ambient temperature in a refrigerator where you have the glass of milk. the temperature of the milk changes with the equation T'(t)=-k(T-Y) where t is time and y is the ambient temperature. the temperature of the milk when it is put in the refridgerator at t=0 is 15 degrees celsius. after one hour the temperature of the milk is 12 degrees. what is the temperature in the fridge?

T'(t)=-k(T-Y)

## The Attempt at a Solution

i have come as far as to determine the constants of T, but to me it seems like there is too little information to determine what the temperature of the fridge must be.

Mons

lanedance
Homework Helper
so i think if you know the original ambient outside temp, you should be able to determine k, then using k & the time/temp change, you should be able to determine the temp of the fridge

so do you know the original outside temp?

i understand, but i wasn't sure when doing this myself if i was "allowed" to use the same value of k both inside and outside the fridge.

lanedance
Homework Helper
yes you can, the k value repesents the dynamics of the cup interacting with an ambient temperature, which applies both within & without the fridge