       Re: how do I solve for this

• To: mathgroup at smc.vnet.net
• Subject: [mg117640] Re: how do I solve for this
• From: Alexei Boulbitch <alexei.boulbitch at iee.lu>
• Date: Tue, 29 Mar 2011 06:51:52 -0500 (EST)

```Say, you do:

p = \[CapitalNu]*kb*T/(V[T] - \[CapitalNu]*b) - a*\[CapitalNu]^2/V[T]^2

-((a \[CapitalNu]^2)/V[T]^2) + (
kb T \[CapitalNu])/(-b \[CapitalNu] + V[T])

der = D[p, T]

(kb \[CapitalNu])/(-b \[CapitalNu] + V[T]) + (
2 a \[CapitalNu]^2 Derivative[V][T])/V[T]^3 - (
kb T \[CapitalNu] Derivative[V][T])/(-b \[CapitalNu] + V[T])^2

sol = Solve[der == 0, V'[T]][[1, 1]]

Derivative[V][T] ->  -((
kb \[CapitalNu] (b \[CapitalNu] - V[T]) V[
T]^3)/(-2 a b^2 \[CapitalNu]^4 + 4 a b \[CapitalNu]^3 V[T] -
2 a \[CapitalNu]^2 V[T]^2 + kb T \[CapitalNu] V[T]^3))

Is it what you had in mind? You remember, of coarse, that you cannot use N as a variable in Mathematica.

Say I have

p=N*kb*T/(V-N*b)-a*N^2/V^2

I want to evaluate the derivative of V with respect to T, keeping p,N,kb,b,a constant.

I understand that this can be done by hand. I just want to know whether this can be done by using mathematica.
I couldnt understand how to use Solve to do this. maybe there is something else I am not aware of

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Alexei Boulbitch, Dr. habil.
Senior Scientist
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