Re: how do I solve for this

• To: mathgroup at smc.vnet.net
• Subject: [mg117637] Re: how do I solve for this
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Tue, 29 Mar 2011 06:51:20 -0500 (EST)
• References: <imfa6a\$io5\$1@smc.vnet.net>

```thinktank1985 wrote:

First make your variables constant (I use n instead of N, because N is a
function, which should not be used as a Variable):

SetAttributes[{p,n,kb,b,a},Constant]

eq = p == (n kb T)/(V - n b) - (a n^2)/V^2

Calculate the total derivative:

totDiff=Dt[eq,T]

Out=
0 == (kb n)/(-b n + V) + (2 a n^2 Dt[V, T])/V^3 -
(kb n T Dt[V, T])/(-b n + V)^2

Solve for Dt[V,T]:

Solve[totDiff,Dt[V,T]] // Together

Out= {{Dt[V, T] -> (kb n (b n - V) V^3)/
(2 a b^2 n^4 - 4 a b n^3 V + 2 a n^2 V^2 - kb n T V^3)}}

> 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
>

--
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

```

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