# Thread: Newtons law of cooling problem

1. ## Newtons law of cooling problem

I need help setting up the following problem.

A freshly brewed cup of coffee has temperature 95 degrees C in a 20 degree C room. When its temperature is 73 degrees C, it is cooling at a rate of 1 degree C per minute. When does this occur?

2. Originally Posted by izzychec
I need help setting up the following problem.

A freshly brewed cup of coffee has temperature 95 degrees C in a 20 degree C room. When its temperature is 73 degrees C, it is cooling at a rate of 1 degree C per minute. When does this occur?
Newton's law of cooling states that the rate of cooling is proportional to the temperature difference between the coffee and its environment.

$\displaystyle \frac{dT}{dt} = k(T - E)$

where $\displaystyle T$ is the coffee's temperature at any time $\displaystyle t$ and $\displaystyle E$ is the temperature of the environment.

you were given the rate of cooling at $\displaystyle T = 73$ ... you should be able to find the proportion constant $\displaystyle k$ using that info.

once you do, separate variables and solve for $\displaystyle T$ as a function of $\displaystyle t$ and solve the problem.