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Math Help - Partial Derivatives with gas, pressure, volume, temperature..

  1. #1
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    Partial Derivatives with gas, pressure, volume, temperature..

    The gas law for a fixed mass m for an ideal gas at absolute temperature T, pressure P, and volume V is PV = mRT, where R is the gas constant.
    Show that бP/бV бV/бT бT/бP = -1


    So basically P = mRT/V, V = mRT/P, T = PV/mR are the different functions, and we take the partial derivative of each...but not totally sure how
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  3. #3
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    Take the partial of each by just treating the others as a constant.

    \frac{{\partial}P}{{\partial}V}=\frac{-mRt}{V^{2}}

    \frac{{\partial}V}{{\partial}T}=\frac{mR}{P}

    \frac{{\partial}T}{{\partial}P}=\frac{V}{mR}

    Multiply them together:

    (\frac{-mRt}{V^{2}})(\frac{mR}{P})(\frac{V}{mR})=\frac{-mRT}{PV}

    But, PV=mRT

    Sub it in:

    \frac{-mRT}{mRT}=-1
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