Related Experiment Video
Updated: Sep 17, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Equation of state of a small system with surface degrees of freedom
Dmitry M Naplekov1, Vladimir V Yanovsky1,2
1Institute for Single Crystals, NAS Ukraine, 60 Nauky Ave., Kharkov 61001, Ukraine.
Abstract:
We considered a model of a small system with internal particles and surface degrees of freedom. All the main statistical distributions were obtained explicitly on a pre-thermodynamic limit basis. The concept of temperature or thermodynamic equations was not used. The distribution of the coordinates of a surface element allows for the rigorous determination of the pressure exerted by the internal particles. In this way, we have derived the exact equation of state for a small system with a surface. It relates the pressure to the numbers of bulk and surface degrees of freedom, their mean energies, and other parameters. The mean potential energy of the surface was found to be higher than the mean kinetic energy per degree of freedom. The obtained equation of state accounts for the influence of this excessive surface energy. In the thermodynamic limit, it transfers to the usual equation of state for an ideal gas.
Related Concept Videos
Equation of State
Equations of Equilibrium in Three Dimensions
According to the vector equations of equilibrium, the vector sum of all the external forces acting on a body must...
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Equation of Motion for a Rigid Body
The combined moments generated about the center of mass of the object are equal to the rate of change of the angular momentum of the body. An external force, when applied at a different...
One-Degree-of-Freedom System
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
Euler Equations of Motion

