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Need a m-file

  1. Mar 6, 2010 #1
    1. The problem statement, all variables and given/known data

    Van der Waals’s equation of state for an imperfect gas is

    ( P + a / v ^ 2) ( v - b ) = R T

    where P is the pressure (atm), v is the molar volume (liters/mole), T is the absolute temperature (K), and a (liter
    2.atm/mol2), and b (liter/mol) are constants that depend on the particular gas. Find
    molar volume of carbon dioxide at 3 atm and 320 K. For carbon dioxide, you may use a=3.592

    and b=0.04267. (Hint: Use ideal gas law to make your initial guess.)

    a) Write a generic MATLAB m-file that uses Newton’s (Newton-Raphson) method to solve for x
    given the function f(x), initial guess x0, and error tolerance es. Make use of the attached
    pseudocode given for the fixed-point iteration method.
    b) Write a MATLAB m-file that uses the generic m-file you have developed in part (a) to solve for
    the molar volume of any gas, given the P, T, R, a, and b. Use a relative error tolerance of
    0.01% for convergence of molar volume.
    c) Run the m-file you have developed in part (b) along with the generic m-file of part (a) for the
    case of carbon dioxide given above. Make sure you display the result at each iteration.
    d) Plot error as a function of the iteration step. Do not forget to label the axes.
    e) MATLAB has a built-in function called fzero to find the real root of a single equation. A
    simple representation of its syntax is
    fzero(function, x0)
    where function is the name of the function being evaluated, and x0 is the initial guess.
    Solve the above problem using fzero. Comment on the result by comparing with the result
    of (c).



    2. Relevant equations



    3. The attempt at a solution
    How can i solve this question?
     
  2. jcsd
  3. Mar 6, 2010 #2

    Päällikkö

    User Avatar
    Homework Helper

    As required by the rules of the homework questions forum, please show your own attempt at a solution.
     
  4. Mar 7, 2010 #3

    Mark44

    Staff: Mentor

    The rules are here: https://www.physicsforums.com/showthread.php?t=5374.

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  5. Mar 7, 2010 #4
    This is my m-file,can you check it,please? I can't see the plot?Why? I use [root]=newtoniandream( ' y ', 1e-3)


    function [f, derf ]=y(v)
    a=3.592; b=0.04267; P=3; T=320; R=0.082;
    f= (P+a/v^2)*(v-b)-R*T;
    derf=P-a/v^2+2*a*b/v^3;


    function [root]=newtoniandream(v0,tol)
    v=v0;
    n=0;
    err=3;
    fprintf('iteration x percent relative error\n')
    while err>tol
    n=n+1;
    [f, derf ]=feval('y',v);
    vnew=v-f/derf;
    err(n)=(abs((vnew-v)/vnew))*100;
    fprintf('%2d %f %f\n',n,vnew,err(n))
    v=vnew;
    plot(n,err)
    hold on
    end
    root=vnew
     
  6. Mar 8, 2010 #5

    Mark44

    Staff: Mentor

    You're not using the plot command correctly. It should be used on two arrays, not on a single pair of coordinates, which means it should probably not be inside your while loop.

    Also, I don't think you are using err correctly. In one line, you set err to 3, but inside your while loop, you treat err as an array.

    Some documentation that might be helpful is here: http://www.mathworks.com/access/helpdesk/help/pdf_doc/matlab/getstart.pdf.

    Ch. 2 deals with data types, including matrices. See Working with Matrices, p. 2-16, and the following pages.

    Ch. 3 deals with plotting. See Using Basic Plotting Functions on page 3-56.

    Ch. 4 deals with Flow Control, including functions. See Functions, page 4-22.
     
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