Shimansky equation

In thermodynamics, the Shimansky equation describes the temperature dependence of the heat of vaporization (also known as the enthalpy of vaporization or the heat of evaporation):
 * $$ L = L_0 \tanh\left( \frac{L T_C}{L_0 T}\right)$$

where:
 * $L$ is the latent heat of vaporization at the temperature $T$,
 * $TC$ is the critical temperature,
 * $L0$ is the parameter that is equal to the heat of vaporization at zero temperature ($T → 0$),
 * $tanh$ is the hyperbolic tangent function.

This equation was obtained in 1955 by Yu. I. Shimansky, at first empirically, and later derived theoretically. The Shimansky equation does not contain any arbitrary constants, since the value of $TC$ can be determined experimentally and $L0$ can be calculated if $L$ has been measured experimentally for at least one given value of temperature $T$. The Shimansky equation describes quite well the heat of vaporization for a wide variety of liquids. For chemical compounds that belong to the same class (e.g. alcohols) the value of $\tfrac{L_0}{T_C}$ ratio remains constant. For each such class of liquids, the Shimansky equation can be re-written in a form of
 * $$ \frac{L}{AT_C} = \tanh\frac{L}{AT}, $$

where $$ A = \tfrac {L_0}{T_C} = \text{const}.$$ The latter formula is a mathematical expression of structural similarity of liquids. The value of $TC$ plays a role of the parameter for a group of curves of temperature dependence of $L$.