# Newton's Law of Cooling of coffee

1. Oct 29, 2009

### ajr246

1. The problem statement, all variables and given/known data
Suppose that a cup of hot coffee at a temperature of 1850 is set down to cool in a room where the temperature is kept at 700. What is the temperature of the coffee 10 minutes later?

2. Relevant equations
f(t)=(T0 - T1))e-kt + T1
where T0 is the initial temperature of the coffee,
T1 is the temperature of the room,
f(t) is the temperature of the coffee after t minutes,
k is a negative constant

3. The attempt at a solution
I am studying precalculus independently. This problem is from Cohen, Precalculus with Unit-Circle Trigonometry, 4th ed.

The problem statement doesn't seem to give enough data to solve it. I can't figure out how to find k in order to find f(t). Is there a technique I'm not seeing?

I've gotten this far:
f(10)=(185-70)e-k10+70
f(10)=115e-10k+70

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 29, 2009

### HallsofIvy

Staff Emeritus
You're right. Since you do not know either k or Q you cannot solve that equation for either one. I suspect that you have copied the problem incorrectly. You have to be given the temperature initially and at some other time in order to find k. Then you can find the temperature for any t.

3. Oct 29, 2009

Thanks.