Skip to main content
Chemistry LibreTexts

4.14: Enthalpy is a State Function

  • Page ID
    390816
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Our expression for internal energy at constant pressure:

    \[\Delta U=q_P+w=q_P-P\Delta V \nonumber \]

    Rearrange:

    \[q_P=\Delta U+P\Delta V=U_2-U_1+P(V_2-V_1) \nonumber \] \[q_P=\left(U_2+PV_2\right)-\left(U_1+PV_1\right) \nonumber \]

    We can define this term as enthalpy:

    \[H\equiv U+PV \nonumber \]

    This is a new state function.


    4.14: Enthalpy is a State Function is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

    • Was this article helpful?