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1.9.4: Entropía- Dependencia de la Temperatura

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    79581

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    Mediante una operación de cálculo, la dependencia isocórica de la entropía de la temperatura se relaciona con la dependencia isobárica correspondiente. Así

    \[\left(\frac{\partial S}{\partial T}\right)_{V}=\left(\frac{\partial S}{\partial T}\right)_{p}-\left(\frac{\partial S}{\partial p}\right)_{T} \,\left(\frac{\partial p}{\partial V}\right)_{T} \,\left(\frac{\partial V}{\partial T}\right)_{p}\]

    Pero

    \[\left(\frac{\partial S}{\partial p}\right)_{T}=-\left(\frac{\partial V}{\partial T}\right)_{p}\]

    Por lo tanto,

    \[\left(\frac{\partial \mathrm{S}}{\partial \mathrm{T}}\right)_{\mathrm{V}}=\left(\frac{\partial \mathrm{S}}{\partial \mathrm{T}}\right)_{\mathrm{p}}+\left(\frac{\partial \mathrm{p}}{\partial \mathrm{V}}\right)_{\mathrm{T}} \,\left[\left(\frac{\partial \mathrm{V}}{\partial \mathrm{T}}\right)_{\mathrm{p}}\right]^{2}\]

    O,

    \[\left(\frac{\partial S}{\partial T}\right)_{V}=\left(\frac{\partial S}{\partial T}\right)_{p}-\frac{\left(E_{p}\right)^{2}}{K_{T}}\]

    El término final en la ecuación (c) contiene la variable\(\mathrm{p}-\mathrm{V}-\mathrm{T}\).

    This page titled 1.9.4: Entropía- Dependencia de la Temperatura is shared under a Public Domain license and was authored, remixed, and/or curated by Michael J Blandamer & Joao Carlos R Reis.