= Water potential
{title2=$\Psi$}
{wiki}
<Water potential> expresses the <chemical potential> of <water> relative to a stated pure-<water> reference in units of <pressure>. For a nearly incompressible liquid at fixed <temperature>, use a constant reference <molar volume> $\bar V_w$ and write
$$
\Psi=\frac{\mu_w-\mu_w^{\mathrm{ref}}}{\bar V_w}.
$$
The reference is pure <water> at the same <temperature> and a chosen <pressure> $P_0$. Both sides must use the same reference. Neglecting height differences and interactions with solid surfaces, the approximation is
$$
\mu_w\simeq\mu_w^{\mathrm{ref}}+RT\ln a_w+\bar V_w(P-P_0),\qquad
\Psi\simeq(P-P_0)+\frac{RT}{\bar V_w}\ln a_w=\Psi_p+\Psi_s.
$$
Here $a_w$ is the dimensionless <thermodynamic activity> of <water>, $R$ the <molar gas constant>, and $T$ the absolute <temperature>. The <natural logarithm> is therefore applied to a dimensionless quantity. The <pressure> contribution $\Psi_p=P-P_0$ increases with <pressure>; the <solute potential> $\Psi_s$ is negative when $a_w<1$. Across an available passive water route, net <water> transfer favors higher to lower <water potential>. The familiar <plant> description adds effects of height and interactions with solid surfaces when they matter; they are omitted in the two liquid compartments here.<Biology 2e by Mary Ann Clark and others/30.5 Transport of Water and Solutes in Plants>[Biology 2e, §30.5, Water Potential, Solute Potential, Pressure Potential and Figure 30.32: component balance and direction of transfer]{ref}
Adding <solute> and raising <pressure> can thus cancel in <water potential> while each contribution remains nonzero. Equality of <water potential> does not imply equality of <pressure> or of every <solute> <concentration>. In a supported <plant> cell, the <cell wall> permits a positive <turgor pressure> to balance a negative <solute potential>; <plasmolysis> illustrates the opposite loss of support after <water> leaves.
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