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Math Help - Algebraic transposition

  1. #1
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    Algebraic transposition

    I have this homework question that I'm having difficulties with. Any help would be most welcome.

    The pressure, p, and volume, v, of a gas undergoing a polytropic process are related by the equation, p_1 v_1^n=p_2 v_2^n where n is the polytropic index.

    If \frac{p_1 v_1}{T_1}= \frac{p_2 v_2}{T_2} determine the expression for p_1, in terms of p_2, T_1, T_2, and n.
    Last edited by Isomorphism; May 26th 2009 at 01:54 PM. Reason: fixed LaTex
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  2. #2
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    Quote Originally Posted by ady72 View Post
    I have this homework question that I'm having difficulties with. Any help would be most welcome.

    The pressure, p, and volume, v, of a gas undergoing a polytropic process are related by the equation, p_1 v_1^n=p_2 v_2^n where n is the polytropic index.

    If \frac{p_1 v_1}{T_1}= \frac{p_2 v_2}{T_2} determine the expression for p_1, in terms of p_2, T_1, T_2, and n.
    (*) \quad p_1 v_1^n=p_2 v_2^n \implies p_1 =p_2 \left(\frac{v_2}{v_1}\right)^n

    (*) \quad \frac{p_1 v_1}{T_1}= \frac{p_2 v_2}{T_2} \implies \frac{v_2}{v_1}= \frac{p_1 T_2}{p_2 T_1}

    Thus p_1 =p_2 \left(\frac{v_2}{v_1}\right)^n = p_2 \left(\frac{p_1 T_2}{p_2 T_1}\right)^n \implies  p_1 = p_2 \left(\frac{T_2}{T_1}\right)^{\frac{n}{n-1}}
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