# Math Help - Newton's Law of Cooling/Warming

1. ## Newton's Law of Cooling/Warming

The problem: A thermometer is taken from inside a room to the outside, where the air temperature is 5 degrees Fahrenheit. After one minute, the thermometer reads 55 degrees Fahrenheit, and after 5 minutes it reads 30 degrees Fahrenheit. What is the initial temperature in the room?

I use: T(t)=Tm-ce^kt

but what is my Tm? would it be 5 degrees Fahrenheit? and if so, won't I still have two unknowns: c and k?

2. Originally Posted by latavee
The problem: A thermometer is taken from inside a room to the outside, where the air temperature is 5 degrees Fahrenheit. After one minute, the thermometer reads 55 degrees Fahrenheit, and after 5 minutes it reads 30 degrees Fahrenheit. What is the initial temperature in the room?

I use: T(t)=Tm-ce^kt

but what is my Tm? would it be 5 degrees Fahrenheit? and if so, won't I still have two unknowns: c and k?
Newton's law of cooling is:

$\frac{dT}{dt}=-k(T-T_{amb})$

Solve this and apply the given tempratures and times to solve for all the unknows in the problem.

( $T_{amb}$ is the ambient tempratur and $T$ is the temprature of the object )

CB