# How can I get this equation?

• Sep 27th 2012, 03:36 PM
Shanter
How can I get this equation?
I need to get dp/p = -a*dT + k*dP.
I have k = -1/V * (δV/δP)
a = 1/V * (δV/δt), a = -1/p * (δp/δT) and p = N/V
Note that p does not equal P.
I'm still working on this, but I'm not making much progress.
• Sep 27th 2012, 04:44 PM
chiro
Re: How can I get this equation?
Hey Shanter.

For dV/dP, use the fact that V=N/p and differentiate (you will have to use the quotient rule if N is not independent from P) which will give something in terms of p.
• Sep 27th 2012, 05:33 PM
Shanter
Re: How can I get this equation?
so if N is not independent than do I get (p(dN/dp) - N)/p^2? I don't see how that helps
• Sep 27th 2012, 06:41 PM
chiro
Re: How can I get this equation?
The point is to get rid of the V's and the other terms not in the expression so you can collect and simplify the terms.

Also I think you can assume N to be indepedent which simplifies things greatly and my reasoning is that if it wasn't it would be labelled N(p) or the expression would be simplified to some grand function of p.
• Sep 27th 2012, 07:57 PM
Shanter
Re: How can I get this equation?
Ok I think I got it now, but I'm not sure about some of the math. I get dp/p = -dV/V from dV/dp of V=N/p. Using a = 1/V * (δV/δt) i get δV = V*a*dT and using k = -1/V * (δV/δP) I get δV = -V*dP*k.
So can does dV = δV+δV here? I get the right answer, but that doesn't feel right to me.