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19.7: Work and Heat Have a Simple Molecular Interpretation

  • Page ID
    13705
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    Statistical interpretation

    We can use what we know about the statistical side of thermodynamics to give a simple interpretation to a change \(dU\):

    we see that because \(\delta w_{rev} = -PdV\)

    Image:CH431_Image67.gif
    Image:CH431_Image68.gif

    See also section 17-5 :In this section it is shown that we can manipulate the partition function to find the pressure of a system by calculating the above moment of the distribution. Again we take the derivative of the logarithm of the partition function \(Q\), this time versus V and show that the result resembles the last equation pretty closely (apart from a factor ). Thus we get:

    Image:CH431_Image69.gif
    Image:CH431_Image70.gif
     

    Once again we can find an important quantity of our system by manipulating the partition function \(Q\).


    19.7: Work and Heat Have a Simple Molecular Interpretation is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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