# Linear Models

• March 11th 2013, 07:13 PM
leonhart
Linear Models
http://mathhelpforum.com/differentia...ody-found.html

That is link to the previous problem posted by another student.

My question is:

The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification is:
http://i45.tinypic.com/35hju4n.png

where k<0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 150 degree F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 100 degree F. If Tm = 70 degree F, then what is the temperature of the coffee cup B after 30 min?

help is greatly appreciated!
• March 16th 2013, 06:41 AM
majamin
Re: Linear Models
Quote:

Originally Posted by leonhart
http://mathhelpforum.com/differentia...ody-found.html

That is link to the previous problem posted by another student.

My question is:

The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification is:
http://i45.tinypic.com/35hju4n.png

where k<0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 150 degree F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 100 degree F. If Tm = 70 degree F, then what is the temperature of the coffee cup B after 30 min?

help is greatly appreciated!

Separate variables:

$\frac{dT}{T-T_m}=kSdt$

Now integrate both sides of the equation.