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List of symbols

Symbol Name of the symbol Unit
$A$ function $ A $ $\mathrm{ }$
$B$ function $ B $ $\mathrm{ }$
$C$ function $ C $ $\mathrm{ }$
$I$ exponent $ I $ $\mathrm{ }$
$J$ exponent $ J $ $\mathrm{ }$
$J^o$ exponent $ J^o $ $\mathrm{ }$
$P_{SV}$ saturated vapor pressure $\mathrm{Pa}$
$R$ specific gas constant of ordinary water $\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$
$T$ the water temperature $\mathrm{°C}$
$T^*$ temperature reducing quantity $\mathrm{K}$
$\text{Region}$ region $\mathrm{ }$
$c_p$ specific isobaric heat capacity $\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$
$c_ν$ specific isochoric heat capacity $\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$
$h$ specific enthalpy $\mathrm{J\cdot kg^{-1}}$
$n$ coefficient $ n $ $\mathrm{ }$
$n^o$ coefficient $ n^o $ $\mathrm{ }$
$p$ the water pressure $\mathrm{Pa}$
$p^*$ pressure reducing quantity $\mathrm{Pa}$
$s$ specific entropy $\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$
$u$ specific internal energy $\mathrm{J\cdot kg^{-1}}$
$w$ speed of sound $\mathrm{m\cdot s^{-1}}$
$α_p$ relative pressure coefficient $\mathrm{K^{-1}}$
$α_ν$ isobaric cubic expansion coefficient $\mathrm{K^{-1}}$
$β_p$ isothermal stress coefficient $\mathrm{kg\cdot m^{-3}}$
$γ$ dimensionless Gibbs free energy $\mathrm{ }$
$γ^o$ ideal-gas part $\mathrm{ }$
$γ^o_{ππ}$ second partial derivative of $ γ^o $ with respect to $ π $ $\mathrm{ }$
$γ^o_{πτ}$ cross derivative of $ γ^o $ with respect to $ π $ and temperature $ τ $ $\mathrm{ }$
$γ^o_{ττ}$ second partial derivative of $ γ^o $ with respect to $ τ $ $\mathrm{ }$
$γ^o_π$ derivative of $ γ^o $ with respect to the dimensionless pressure $ π $ $\mathrm{ }$
$γ^o_τ$ partial derivative of $ γ^o $ with respect to $ τ $ $\mathrm{ }$
$γ^r$ residual part $\mathrm{ }$
$γ^r_{ππ}$ second partial derivative of $ γ^r $ with respect to $ π $ $\mathrm{ }$
$γ^r_{πτ}$ cross derivative of $ γ^r $ with respect to $ π $ and temperature $ τ $ $\mathrm{ }$
$γ^r_{ττ}$ second partial derivative of $ γ^r $ with respect to $ τ $ $\mathrm{ }$
$γ^r_π$ derivative of $ γ^r $ with respect to the dimensionless pressure $ π $ $\mathrm{ }$
$γ^r_τ$ partial derivative of $ γ^r $ with respect to $ τ $ $\mathrm{ }$
$γ_{ππ}$ second partial derivative of $ γ $ with respect to $ π $ $\mathrm{ }$
$γ_{πτ}$ cross derivative of $ γ $ with respect to $ π $ and temperature $ τ $ $\mathrm{ }$
$γ_{ττ}$ second partial derivative of $ γ $ with respect to $ τ $ $\mathrm{ }$
$γ_π$ derivative of $ γ $ with respect to the dimensionless pressure $ π $ $\mathrm{ }$
$γ_τ$ partial derivative of $ γ $ with respect to $ τ $ $\mathrm{ }$
$δ$ reduced density $\mathrm{ }$
$θ$ reduced temperature $\mathrm{ }$
$θ$ transformed temperature $\mathrm{ }$
$κ_T$ isothermal compressibility $\mathrm{Pa^{-1}}$
$ν$ specific volume $\mathrm{m^3\cdot kg^{-1}}$
$π$ reduced pressure $\mathrm{ }$
$ρ$ mass density $\mathrm{kg\cdot m^{-3}}$
$ρ^*$ mass density reducing quantity $\mathrm{kg\cdot m^{-3}}$
$τ$ inverse reduced temperature $\mathrm{ }$
$φ$ dimensionless Helmholtz free energy $\mathrm{ }$
$φ_{δδ}$ second partial derivative of $ φ $ with respect to $ δ $ $\mathrm{ }$
$φ_{δτ}$ cross derivative of $ φ $ with respect to $ δ $ and temperature $ τ $ $\mathrm{ }$
$φ_{ττ}$ second partial derivative of $ φ $ with respect to $ τ $ $\mathrm{ }$
$φ_δ$ derivative of $ φ $ with respect to the dimensionless density $ δ $ $\mathrm{ }$
$φ_τ$ partial derivative of $ φ $ with respect to $ τ $ $\mathrm{ }$