Re: Solution of this equation

• To: mathgroup at smc.vnet.net
• Subject: [mg20685] Re: Solution of this equation
• From: Dave Richardson <dhr at glue.umd.edu>
• Date: Sun, 7 Nov 1999 02:10:16 -0500
• Organization: University of Maryland
• References: <7vrc3p\$2nd@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Ok, I apologize,

I was Very vague with this question, and a couple of people have been nice
enough to try and help me anyway!

Here is a better statement of the problem and a picture for those interestd:

Thanks in advance!

I guess I was a little misleading (shortsighted actually).

This equation is a thermodynamic function.

I should have said Over its solution domain, it has 3 real roots.

I need to use the roots as variable limits of integration to solve for a Pr
that meets constraints.

So, I guess there is the possibility of imaginary roots, I am looking to
exclude that posibility.

Sorry I was vague.

Pr is the reduced pressure, P/Pcritical.  In this case 0 <= Pr <= 1.
Also, Tr is the reduced Temperature T/Tcritical.  In this case 0 <= Pr <= 1.

For a unique Tr, There will be 3 real roots for vr (at a specific Pr).

I need to find the value Pr, which will meet the following condition:

Integral (Pr, {vr, vr(smallest root), vr(middle Root)}) + Integral (Pr, {vr,
vr(middle root), vr(largest Root)}) = 0

Here is a picture [email the author to get the picture - mod],
if you are really interested in the problem.

Dave Richardson wrote:

> 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...
>
> Any help?
>
> Thanks,
>
> Dave!
>
> --
> Dave Richardson
> University of Maryland
> Department of Mechanical Engineering
> Center for Environmental Energy Engineering
> (301) 405-8726
> dhr at glue.umd.edu

--
Dave Richardson
University of Maryland
Department of Mechanical Engineering
Center for Environmental Energy Engineering
(301) 405-8726
dhr at glue.umd.edu

```

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