Thermodynamics of Soil Moisture

Soil water potential: A historical perspective and recent breakthroughs

“…Then Equation becomes $$\begin{equation} - \Delta G > \Delta {W_{\rm{m}}}\end{equation}$$which illustrates that the decrease in value of Gibbs function represents the maximum nonexpansion work obtainable from a system in a process under constant T and P . Consequently, the Gibbs function is also commonly called Gibbs free energy or free energy in the literature (same for the Helmholtz function), mainly due to its historical origin with conversion between heat and mechanical work in steam engines (Chatelain, 1949; Epstein, 1937). Nevertheless, although all quantities in Equation have the dimension of energy, the Gibbs function itself is not conserved during an irreversible process, rendering the word “free energy” inappropriate and causing great confusion in practical applications adopted by different research fields (Bazhin, 2012; Schroeder, 2000).…”

“…Generally, the potential energies of a system as a whole do not affect the internal energy that the system possesses. It is thus more appropriate to not consider the potentials due to the existence of external force fields (e.g., most commonly gravitational force) as part of the traditional chemical potential defined in thermodynamics (Babcock & Overstreet, 1955; Chatelain, 1949). For situations where external force fields X are considered, Bolt and Frissel (1960) defined a quantity called partial specific free energy $${\bar{G}_i}$$ for the i th constituent of the system as $$\begin{equation}{\overline{G}_i} = {\left( {\frac{{\partial G}}{{\partial {m_i}}}} \right)_{T,P,\left\{ {{m_{j \ne i}}} \right\},X}} \ne {\left( {\frac{{\partial G}}{{\partial {m_i}}}} \right)_{T,P,\left\{ {{m_{j \ne i}}} \right\}}} = {\mu _i}\end{equation}$$where the partial specific free energy $${\bar{G}_i}$$ was clearly distinguished from the concept of chemical potential due to the inconsistency in fundamental definition.…”

“…Two major potential energies are commonly identified in soil: gravitational potential energy d W g and electromagnetic potential energy d W em , according to the types of interactions between water molecules and the external force fields. Consequently, the total static energy of a soil–water–air REV can be described by a general characteristic function dΨ defined as the sum of Gibbs function d G (internal) and potential energy function dΦ (external) due to energy conservation (e.g., Chatelain, 1949; Groenevelt & Bolt, 1969; Iwata, 1972b; Low, 1951): $$\begin{equation} \def\eqcellsep{&}\begin{array}{c} {\rm{d}}\psi = {\rm{d}}G + {\rm{d}}\Phi = V{\rm{d}}P\\ + \sum\nolimits_i {{\mu _i}} {\rm{d}}{m_i} + \gamma {\rm{d}}{A_{{\rm{aw}}}} + {\rm{d}}{W_{\rm{g}}} + {\rm{d}}{W_{{\rm{em}}}} \end{array} \end{equation}$$Referenced to the pure water at standard state (i.e., Ψ 0 = 0), the infinitesimal change in Ψ for the soil water (i.e., dΨ) represents the current energy state of the soil–water–air REV. Consequently, the total soil water potential ψ t , which can be recognized as the intensive form of the characteristic function Ψ, is derived in a similar way to the definition of chemical potential (Equation ) as …”

“…The so‐called chemical potential (or the specific Gibbs free energy) that is defined through a continuously extended way no longer has the same meaning as the one originally used by Gibbs. Instead, the thermodynamic potential functions defined as such are completely new characteristic functions customized for solving specific problems, as has been pointed out by many researchers (Babcock, 1963; Bear & Nitao, 1995; Bolt & Frissel, 1960; Chatelain, 1949; Low, 1951; Low & Deming, 1953; Sposito, 1975). Therefore, misuse of the concept of chemical potential should be avoided to prevent confusion in future studies of soil–water potential for unsaturated soil.…”

“…Generally, the potential energies of a system as a whole do not affect the internal energy that the system possesses. It is thus more appropriate to not consider the potentials due to the existence of external force fields (e.g., most commonly gravitational force) as part of the traditional chemical potential defined in thermodynamics (Babcock & Overstreet, 1955;Chatelain, 1949). For situations where external force fields X are considered, Bolt and Frissel (1960) defined a quantity called partial specific free energy Ḡ𝑖 for the ith constituent of the system as…”