Diffy Q word problem

bearej50 · #1 $Old$ November 5th, 2009, 05:59 PM

A cool object is placed in a room that is maintained at a constant temperature of 20° C. The rate at which the temperature of the object rises is proportional to the difference between the room temperature and the temperature of the object. Let y = f(t) be the temperature of the object at time t, and give a differential equation that describes the rate of change of f(t).

jfortiv · #2 $Old$ November 5th, 2009, 07:59 PM

Ok. Let's break this up into pieces...

The rate at which the temperature of the object rises: $\frac{dy}{dt}$

Room temperature: $\sigma_{room}$

The difference between the room temperature and the temperature of the object: $\sigma_{room} - y$

Proportion: $k$

All together now: $\frac{dy}{dt}=k($ $\sigma_{room} - y)$

Does the process that I used to generate this equation make sense to you? If not, ask me a question. I'll help.

bearej50 · #3 $Old$ November 5th, 2009, 08:53 PM

perfect sense!!!