Differential Equation Problem

  • Thread starter Chrismb159
  • Start date
  • #1
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?
 

Answers and Replies

  • #2
Tide
Science Advisor
Homework Helper
3,089
0
What have you tried so far?
 
  • #3
93
0
To solve you may use Newton's law of cooling

[tex] \int_{T_{0}}^{T} \frac{dT}{T-T_{s}} = - \kappa \int_{t_{0}}^{t} d t^{\prime} [/tex]

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
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.
 

Related Threads on Differential Equation Problem

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
865
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
522
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
7
Views
784
Top