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- W1969331882 startingPage "5012" @default.
- W1969331882 abstract "A set of tensorial thermodynamic substate variables ${V}_{mathrm{ij}}$ has been found such that under hydrostatic pressure the enthalpy $H$ of a solid, defined by $Hensuremath{equiv}Uensuremath{-}{ensuremath{tau}}_{mathrm{ij}}{V}_{mathrm{ij}}$, where ${ensuremath{tau}}_{mathrm{ij}}ensuremath{equiv}{(frac{ensuremath{partial}U}{ensuremath{partial}{V}_{mathrm{ij}}})}_{S}$, reduces to the conventional enthalpy $U+pV$. $U$ is the internal energy per unit mass, $p$ the pressure, $V$ the specific volume, and $S$ the entropy per unit mass. Previously used tensorial variables (e.g., the Lagrangian strain components) lead to a different enthalpy. The new variables are defined by ${V}_{mathrm{ij}}=(frac{1}{3overline{ensuremath{rho}}}){{D}^{(frac{3}{2})}}_{mathrm{ij}}$, ${D}_{mathrm{ij}}=(frac{ensuremath{partial}{x}_{k}}{ensuremath{partial}{X}_{i}})(frac{ensuremath{partial}{x}_{k}}{ensuremath{partial}{X}_{j}})$. Here the ${X}_{i}$ are the Cartesian coordinates of the particles of the body in some arbitrarily stressed reference configuration of density $overline{ensuremath{rho}}$ and stresses ${overline{T}}_{mathrm{ij}}$, ${x}_{i}$ are the present coordinates, and ${{D}^{(frac{3}{2})}}_{mathrm{ij}}$ is a symbol for the $mathrm{ij}$ element of the positive real 3/2 power of the tensor ${D}_{mathrm{ij}}$. Under these definitions, the enthalpy of a solid of arbitrary symmetry has been proved to reduce to $U+pV$ whenever x and X both correspond to states in which the stress in hydrostatic pressure. As a special case, X may of course be an unstressed configuration. The above choice of variables is not unique. In fact, the enthalpy reduces to $U+pV$ if ${V}_{mathrm{ij}}$ is any matrix function of ${D}_{mathrm{ij}}$ whose determinant is proportional to the 3/2 power of the determinant of the matrix ${D}_{mathrm{ij}}$. However, the above choice of ${V}_{mathrm{ij}}$ has the additional desirable property that when evaluated at x = X, the thermodynamic tensions ${ensuremath{tau}}_{mathrm{ij}}$ equal the stresses ${T}_{mathrm{ij}}$. In the case of cubic crystals and isotropic media under hydrostatic pressure, the present ${V}_{mathrm{ij}}$ and ${ensuremath{tau}}_{mathrm{ij}}$ reduce to ${V}_{mathrm{ij}}=frac{1}{3}V{ensuremath{delta}}_{mathrm{ij}}$, ${ensuremath{tau}}_{mathrm{ij}}=ensuremath{-}p{ensuremath{delta}}_{mathrm{ij}}$." @default.
- W1969331882 created "2016-06-24" @default.
- W1969331882 creator A5072694303 @default.
- W1969331882 date "1970-12-15" @default.
- W1969331882 modified "2023-09-25" @default.
- W1969331882 title "Thermodynamic Substate Variables for a Solid" @default.
- W1969331882 cites W2067402674 @default.
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- W1969331882 doi "https://doi.org/10.1103/physrevb.2.5012" @default.
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