9.10: A Slightly Philosophical Digression on Energy and Entropy
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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 \(S\).