I solved this problem, but the answer doesn't match with the one supplied in the book. Here's the problem:

if the temperature is kept constant, the relationship between p and V of gas in a ballon is:

pV = K

Where K is a constant. If p = 40 lb/in^2 and is changing at a rate of 2 lb/in^2 per minute, find the rate at which V is changing when V = 100 in^3!

My solution:

pV = K
then V = K/p
dV/dt = d(Kp^(-1))/dt
because K is a constant...
dV/dt = K d(p^(-1))/dt
dV/dt = -Kp^(-2) dp/dt
because K = pV, the equation becomes
dV/dt = -Vp^(-1) dp/dt
dV/dt = -V/p dp/dt

noting that V = 100 in^3, p = 40 lb/in^2, and dp/dt = 2 lb/in^2 per minute, then....

dV/dt = -100/40*2
dV/dt = -5 in^3/min

the book's answer is -50 in^3/min. Did I do something wrong?

i got the same thing as you

pV=k
dp/dt * V + P * dV/dt = 0
2 lb/min * in^2 * 100 in^3 +40 lb/in^2 * dV/dt = 0
200 lbin/min = -40lb/in^2 * dV/dt
-5 in^3/min = dV/dt

Wow, just looking over this problem shows me how far I have until I'm ready for Calculus. :o

You know where to find help ;)

Don't you see this was just a printing error, instead of putting 5 they typed 50???

Emfuser! :wavey:

Thanks guys :)...