# Diff eqs

1. Mar 30, 2006

### Gale

my biggest problem is the word problems. i can't figure out how to write the equation so that i can do the math...

Heat is escaping at a constant rate (dQ/dt is constant) through the walls of a long cylindrical pipe. Find the temperature T at a distance r from the axis of the cylinder if the inside wall has a radius r=1 and a temperature T=100, and the outside wall has r=2 and T=0.

so i couldn't figure out how to model this. dQ/dt= C doesn't get you very far... maybe cause i'm not sure how to relate the heat to temperature.

then i had another problem:

A substance evaporates at a rate proportional to the exposed surface. If a spherical mothball of radius 1/2 sm has a radius .4cm after 6 months, how long will it take for the radius to be 1/4cm?

i started with like dS/dt= k(SA), where S is the amount of substance and SA was the surface area, (which for a sphere is dependent on r, so this was looking good) but then i got confused about whether i need a negative sign or what else because the substance is lessening. then i wondered if the negative would be just be inherent in the solution, cause it ought to be i thought... i don't know. i'm just getting confused.

2. Mar 30, 2006

### devious_

I'm not a physicist, but I think if S is entropy then dQ = T dS.

You need a minus sign for your second equation because we want the rate of decrease of the substance, and not the rate of increase.