       Re: Solution of this equation

• To: mathgroup at smc.vnet.net
• Subject: [mg20700] Re: [mg20629] Solution of this equation
• From: "Kevin J. McCann" <kevinmccann at Home.com>
• Date: Mon, 8 Nov 1999 02:48:45 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```The problem is based on the Maxwell construction in thermodynamics.  At a
given reduced temperature Tr there are 3 real roots for only a limited range
of reduced pressures.  In general the roots are complex.

Kevin

<BobHanlon at aol.com> wrote in message news:8037bu\$adu at smc.vnet.net...
> Dave,
>
> Whether or not the solutions are all real or the imaginary parts are very
> small will depend on the values of Pr and Tr. [Note that Tr is a protected
> symbol name for the trace of a matrix or tensor list.]
>
> If you are solving this with specific values and the imaginary parts are
> truly small, then use Chop.
>
> Bob Hanlon
>
>
> In a message dated 11/4/1999 8:04:15 AM, dhr at glue.umd.edu writes:
>
> >Can anyone offer insight here?
> >
> >This Mathematica expression gives 3 solutions to the equation.
> >
> >Solve[Pr == (8*Tr)/(3*vr - 1) - 3/vr^2, vr]
> >
> >
> >The problem is that there are 3 Real solutions, and Mathematica is giving
> >solutions with (granted a small) imaginary component.
> >
> >And hitting it with  a full simplify is just not a good idea...
> >
>

```

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