Re: 2 problems!

*To*: mathgroup at smc.vnet.net*Subject*: [mg120330] Re: 2 problems!*From*: W Craig Carter <ccarter at mit.edu>*Date*: Tue, 19 Jul 2011 06:56:15 -0400 (EDT)*References*: <201107181014.GAA26923@smc.vnet.net>

Hello Mary, Before giving you a brief answer, it looks like you are exploring the critical points of a van der Waals gas. I have a fairly complete mathematica notebook to do this---I use it for teaching--and demonstrates how one should rescale the van der Waals equation. If you would like a copy, contact me directly. I don't recommend continuing on the path that you are following, but here are some pointers to help you learn some mathematica-ology. There are several things you can do immediately to help your code. 1. Avoid using upper case first letters for your own variables. 2. Take a look at your intermediate output in your Do[] (btw, I think you meant to loop over u and w). 3. Note the form of one of your intermediate expressions: sol = Solve[Rationalize[der1 && der2 && p, 0], {a, b, V}, Reals] // N This is a long set of six solutions that has Root[] functions in them for subsequent numerical processing. You probably would be better off writing a function that takes arguments for u_ and w_, and then uses NSolve to get your solution. You don't need to use the Rationalize here. Note the form of one of your intermediate solutions: N[({a, b, V} /. sol) /. {u -> 10, w -> 12}] 4. You get one real solution and the others are undefined. You will want an automatic method of picking out your real solution. Here is an example: Cases[N[({a, b, V} /. sol) /. {u -> 10, w -> 12}], {_Real, _Real, _Real}] I don't follow what you had intended for this expression: \[CapitalPsi] -> a; in your Do[]. Also, I don't think your values of a,b, and V are changing in your loop, so there is no need to recompute the solution each iteration. 5. Collect your solutions into a table: sol = Solve[Rationalize[der1 && der2 && p, 0], {a, b, V}, Reals] // N; abV = {a, b, V} /. sol vdwSolutions = Table[Cases[N[abV /. {u -> ui, w -> 12}], {_Real, _Real, _Real}],{ui,-100,100,.01,{vi,-100,100,.01}] 6. Then export your data to excel if you wish Export["solutions.xls", vdwSolutions] Again, This isn't the solution path I recommend.... Kind Regards, W Craig Carter Professor of Materials Science, MIT On Jul 18, 2011, at Mon, Jul 18, 11 ---6:14 AM, Mary R wrote: > Hi to everyone! > I've got two problems that for me is quite difficult... > 1. I want to calculate in the same cicle Do this coefficient a,b,V and > evaluate the difference beetween this calculate coefficient and the real > parameter areal,breal,Vreal and evaluate a coefficient Omega. > I was able to calculate only the coefficient a,b,V; > e.g. > value u , w {2,2}:= > {{{a->-2.57258*10^7,b->-1108.81,V->679.954},{a->1.59736*10^6,b->-210.798,V->380.617},{a->1.3548*10^7,b->53.9538,V->292.367}}, > *3.03895*10^-8 a*,-*3.34268*10^12+a,128465. +b,-200+V*} > can you hel me? > 2. The second problem is to change the result from InputForm in a table to > export in Excel; > that is trasform my result > (e.g.) > value u , w {2,2}: = {{{a->-2.57258*10^7,b->-1108.81,V->679.954},{a->1.59736*10^6,b->-210.798,V->380.617},{a->1.3548*10^7,b->53.9538,V->292.367}},3.03895*10^-8 > a,-3.34268*10^12+a,128465. +b,-200+V} > in a table! > ---------------------listing----------------------- > pression = (R Subscript[T, c])/(V - b) - a/( > b^2 w + b u V + V^2) /. {Subscript[T, c] -> 425.1, R -> 83.14}; > der1 = D[pression, V] == 0; > der2 = D[pression, {V, 2}] == 0; > p = 37.96 - pression == 0; > Vreal = 200; > areal = 3.3426778202443823`*^12; > breal = -128465.27253980785`; > \[CapitalPsi] = \!\(TraditionalForm\` > \*FractionBox[\(a\ P\), \( > \*SuperscriptBox[\(R\), \(2\)]\ > \*SuperscriptBox[\(T\), \(2\)]\)]\ /. {T -> 425.1, \ \ R -> 83.14, > P -> 37.96}\); > Do[sol = Solve[Rationalize[der1 && der2 && p, 0], {a, b, V}, > Reals] // N; \[CapitalPsi] -> a; A = a - areal; B = b - breal; > volume = V - Vreal; > Print[ "value u , w, Omega,difference ", {u, w}, > ": ", {sol, \[CapitalPsi], A, B, volume}], {u,-100, 100,0.1}, {u,-100, > 100,0.1}] > {a, b, V} /. sol > > Thanks a lot in advance for your help. > MR > >

**References**:**2 problems!***From:*Mary R <mathematica023@gmail.com>