Skip to main content
Chemistry LibreTexts

9.10: A Slightly Philosophical Digression on Energy and Entropy

  • Page ID
    152085
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    The content of the first law of thermodynamics is that there is a state function, which we call energy, which has the property that \(\Delta E_{universe}=0\) for any process that can occur. The content of the second law is that there is a state function, which we call entropy, which has the property that \(\Delta S_{universe}>0\) for any spontaneous process.

    These two state functions exhaust the range of independent possibilities: Suppose that we aspire to find a new and independent state function, call it \(B\), which further characterizes the possibilities open to the universe. What other condition could B impose on the universe—or vice versa? The only available candidate might appear to be \(\Delta B_{universe}<0\). However, this does not represent an independent condition, since its role is already filled by the quantity \(-\Delta S_{universe}\).

    Of course, we can imagine a state function, \(B\), which is not simply a function of \(S\), but for which

    \(\Delta B_{universe}>0\), \(\Delta B_{universe}=0\), or \(\Delta B_{universe}<0\), according as the process is spontaneous, reversible, or impossible, respectively. For any given change, \(\Delta B\) would not be the same as \(\Delta S\); however, \(\Delta B\) and \(\Delta S\) would make exactly the same predictions. If \(\Delta B_{universe}\) were more easily evaluated than \(\Delta S_{universe}\), we would prefer to use \(B\) rather than \(S\). Nevertheless, if there were such a function \(B\), its role in our description of nature would duplicate the role played by \(S\).


    This page titled 9.10: A Slightly Philosophical Digression on Energy and Entropy is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Paul Ellgen via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.