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