# Differential Equation Problem

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?

Tide
Homework Helper
What have you tried so far?

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

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.