# Differential Equation Problem

1. Mar 5, 2006

### Chrismb159

hi, i am having trouble with this problem...

An apple cobbler is taken out of the oven at 7:00PM one Saturday night. At that time it is piping hot at 100C. At 7:10PM its temperature is 80C, and at 7:20pm, it is 65C. What is the temperature of the kitchen in which the apple cobbler is being held?

2. Mar 5, 2006

### Tide

What have you tried so far?

3. Mar 5, 2006

### xman

To solve you may use Newton's law of cooling

$$\int_{T_{0}}^{T} \frac{dT}{T-T_{s}} = - \kappa \int_{t_{0}}^{t} d t^{\prime}$$

where To is the initial temperature, Ts is the temperature of the environment (which is what we are after), k is a material constant, etc. Integrate both sides of this equation, and solve for T, and use the three boundary conditions to solve. You should get a reasonable answer for the room temperature. hope this helps, sincerely x

4. Mar 5, 2006

### Chrismb159

thank you for that, we recently learned about that in physics but for some reason i couldnt put 2 and 2 together, i was going in a completely different direction.