A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
When an object is removed from a furnace and placed in an environment with a constant temperature of 90 degrees Fahrenheit , its core temperature is 1120 degrees Fahrenheit . Find the core temperature 5 hours after the object is removed from the furnace.
anonymous
 5 years ago
When an object is removed from a furnace and placed in an environment with a constant temperature of 90 degrees Fahrenheit , its core temperature is 1120 degrees Fahrenheit . Find the core temperature 5 hours after the object is removed from the furnace.

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This should be an application of Newton's Law of Cooling. The law says that the rate of change in the temperature of the object is proportional to the difference between the object temperature and the environment; that is,\[\frac{dT}{dt}=k(TT_{\infty})\]where k is positive, T is the object temperature and T_{infinity} that of the environment. This is a separable equation and you have\[\frac{dT}{TT_{\infty}}=kdt \rightarrow \log(TT_{\infty})=kt+c\]Exponentiating both sides gives,\[TT_{\infty}=Ce^{kt} \rightarrow T= Ce^{kt}+T_{\infty}\]At t=0, the temperature of the object is its initial temperature, and so,\[T(0)=C+T_{\infty} \rightarrow C=T(0)T_{\infty}\]Your equation is then\[T(t)=[T(0)T_{\infty}]e^{kt}+T_{\infty}\]Now, the problem you have here is that there isn't enough information to extract a numerical answer. We need some more info. to find k. From what you do have,\[T(t)=(112090)^oFe^{kt}+90^oF\]\[=(1030^oF)e^{kt}+90^oF\]At t=5 hours,\[T(5)=(1030^oF)e^{5k}+90^oF\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.