       Re: how do I solve for this

• To: mathgroup at smc.vnet.net
• Subject: [mg117677] Re: how do I solve for this
• From: Gary Wardall <gwardall at gmail.com>
• Date: Tue, 29 Mar 2011 06:58:48 -0500 (EST)
• References: <imfa6a\$io5\$1@smc.vnet.net>

```On Mar 24, 6:33 am, thinktank1985 <di... at umich.edu> wrote:
> 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 t=
his 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

For an explicit form try:

-D[N*kb*T/(V - N*b) - a*N^2/V^2 - p, T]/
D[N*kb*T/(V - N*b) - a*N^2/V^2 - p, V]

For an implicit form try:

"First branch"
D[Solve[p == N*kb*T/(V - N*b) - a*N^2/V^2, V][][][], T]
"Second branch"
D[Solve[p == N*kb*T/(V - N*b) - a*N^2/V^2, V][][][], T]
"Third branch"
D[Solve[p == N*kb*T/(V - N*b) - a*N^2/V^2, V][][][], T]

If my calculus is ok.

Gary

```

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