# Newton's Law of Cooling problem

1. Apr 8, 2009

### jackleyt

1. The problem statement, all variables and given/known data
The temperature T of a cup of coffee is a function T(t) where t is the time in minutes. The room temperature is 20 ^\circ Celsius. The rate at which the coffee cools down is proportional to the difference between the temperature of the coffee and the room temperature. Use this information to write a differential equation describing the derivative of the coffee temperature in terms of T and t. Use C as your proportionality constant. C should be a positive number. Write T instead of T(t).

2. Relevant equations

3. The attempt at a solution
I don't know where to start.

2. Apr 8, 2009

### Happyzor

Re: Derivatives

I'm pretty sure this is Newton's Law of Cooling. The problem states that the change in temperature(derivative) is proportional(C) to the difference between the two temps(TempCoffee-20).

So the equation would look like Change in Temp=(Proportional Constant)X(Difference in temperature).

From there, you get your DT and T to the same side and integrate. The solution involves ln and e. Good luck!