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Math Help - Substituting values and solving for an unknown

  1. #1
    Newbie
    Joined
    Nov 2008
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    7

    Substituting values and solving for an unknown

    please give me a solution
    i need to find the value of V in the following equation
    (p+(a/V^2))*(V-b)=RT
    where
    P=9500KPa
    R=.2968Kj/k/kg
    T=175 K
    a=27R^2*Tcr^2?(64*Pcr)
    b=(R*Tcr)/(8Pcr)
    Tcr=136.2 K
    Pcr=3.39MPa
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  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570

    Numerical solution of equations

    Hello self_shattered
    Quote Originally Posted by self_shattered View Post
    please give me a solution
    i need to find the value of V in the following equation
    (p+(a/V^2))*(V-b)=RT
    where
    P=9500KPa
    R=.2968Kj/k/kg
    T=175 K
    a=27R^2*Tcr^2?(64*Pcr)
    b=(R*Tcr)/(8Pcr)
    Tcr=136.2 K
    Pcr=3.39MPa
    (p+(a/V^2))(V-b)=RT

    \Rightarrow (pV^2+a)(V-b)=RTV^2

    \Rightarrow pV^3-(b+RT)V^2+aV-ab=0

    The best advice I can give now is to use a numerical method; e.g. Newton-Raphson, with f(V)= pV^3-(b+RT)V^2+aV-ab and f'(V) = 3pV^2-2(b+RT)V+a.

    I'm not sure what the numerical values are, especially
    a=27R^2*Tcr^2?(64*Pcr)
    What does ? mean?

    If you don't know how to use Newton-Raphson, work out the numerical values of
    p, a, b, R, T (don't bother with the units, they only confuse things); post them here, and I'll do it for you.

    Grandad
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