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1.8.3: Enthalpy- Thermodynamic Potential

  • Page ID
    374770
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    The enthalpy \(\mathrm{H}\) of a closed system is related by definition to the thermodynamic energy \(\mathrm{U}\); \(\mathrm{H}=\mathrm{U}+\mathrm{p} \, \mathrm{V}\). But

    \[\mathrm{dH}=\mathrm{q}+\mathrm{V} \, \mathrm{dp}\]

    From the second law of thermodynamics,

    \[\mathrm{T} \, \mathrm{dS}=\mathrm{q}+\mathrm{A} \, \mathrm{d} \xi ; \quad \mathrm{A} \, \mathrm{d} \xi \geq 0\]

    Then

    \[\mathrm{dH}=\mathrm{T} \, \mathrm{dS}+\mathrm{V} \, \mathrm{dp}-\mathrm{A} \, \mathrm{d} \xi ; \mathrm{A} \, \mathrm{d} \xi \geq 0\]

    Thus all spontaneous processes at constant entropy and pressure (i.e. isentropic and isobaric) lower the enthalpy of a closed system. This conclusion finds application in acoustics where the changes in a system perturbed by a travelling sound wave are discussed in terms of changes in enthalpy at constant entropy and pressure. Confining our attention to systems either at equilibrium (i.e. \(\mathrm{A} = 0\)) or at fixed \(\xi\), two key relationships follow from equation (c).

    \[\mathrm{T}=(\partial \mathrm{H} / \partial \mathrm{S})_{\mathrm{p}}\]

    and

    \[\mathrm{V}=(\partial \mathrm{H} / \partial \mathrm{p})_{\mathrm{S}}\]

    In these terms the extensive variable, volume, is given by the

    1. isentropic differential dependence of enthalpy on pressure, and
    2. isothermal differential dependence of Gibbs energy on pressure.

    This page titled 1.8.3: Enthalpy- Thermodynamic Potential is shared under a Public Domain license and was authored, remixed, and/or curated by Michael J Blandamer & Joao Carlos R Reis.

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