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Math Help - Re-arranging an equation.

  1. #1
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    Re-arranging an equation.

    Need help with a question guys, any help will be most appreciated.

    The pressure, p, and volume, V, of a gas undergoing a polytropic process are related by the equation:


    p1V1n = p2V2n

    where n is the polytropic index.

    If p1V1/ T1 = p2V2/ T2

    determine and expression for p1 in terms of p2 , T1, T2 and n


    It has got me a bit stumped guys so any help would be most appreciated.

    Thanks
    Last edited by mr fantastic; December 20th 2010 at 07:18 PM. Reason: Moved a question to another thread, re-titled.
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  2. #2
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    The pressure, p, and volume, V, of a gas undergoing a polytropic process are related by the equation:


    p1V1n = p2V2n


    where n is the polytropic index.

    Ifp1V1/ T1 = p2V2/ T2

    determine and expression for p1 in terms of p2 , T1, T2 and n
    From the last equation, \displaystyle p_1=p_2\frac{T_1}{T_2}\frac{V_2}{V_1}, so we have to find \displaystyle\frac{V_2}{V_1}. From the first equation, \displaystyle\left(\frac{V_2}{V_1}\right)^n=\frac{  p_1}{p_2}. By taking root of degree n of both sides, you can find V_2/V_1.

    A remark concerning notation. As is standard, use * for multiplication (it can be omitted in certain cases like 3x) and ^ for exponentiation. Otherwise, it is not clear if your p1V1n means p_1V_1n or p_1V_1^n.
    Last edited by mr fantastic; December 20th 2010 at 01:05 PM.
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  3. #3
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    math help please

    Dear Dan Brown,
    I assume you have a chemistry problem and cannot get into the Chemistry Forum. If you describe your problem I will try to help


    bjh
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  4. #4
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    so does V2/V1=(p1/p2)^1/n

    and

    p1 = p2T1/T2*(p1/p2)^1/n
    Last edited by dt71; February 11th 2011 at 03:34 AM.
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  5. #5
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    Yes.
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  6. #6
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    Therefore
    p1 = (p2T1p1^1/n)/T2p2^1/n

    If I divide by p1^1/n

    P1/P1^1/n = p2T1/T2p2^1/n

    This is were i'm stuck
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  7. #7
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    This is were i'm stuck
    What are you trying to do? The original problem was to "determine an expression for p1 in terms of p2 , T1, T2 and n". This has been done in post #4.
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  8. #8
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    but i still have p1 on both sides of the equation, i need to make p1 the subject
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  9. #9
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    Sorry, you are right, of course.

    So, we have \displaystyle\frac{p_1}{p_1^{1/n}}=\frac{p_2}{p_2^{1/n}}\frac{T_1}{T_2}, i.e., \displaystyle p_1^{(n-1)/n}=p_2^{(n-1)/n)}\frac{T_1}{T_2}. Raising both sides to n/(n-1), we get \displaystyle p_1=p_2\left(\frac{T_1}{T_2}\right)^{n/(n-1)}.
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  10. #10
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    rearanging an equation

    PV^n = constant is used to calculate one unknown.polytropic process n=1.395
    P1V1/T1 = P2V2/T2 is used to calculate a temperature
    Example V1=12.48 cu ft V2=5.0 cu ft V1@ 70 F
    P1 = 14.7 psia P2 = 52.6psia t=301F



    bjh
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