Inner Pressure and Inner Energy of the Liquid

The formulas of inner pressure and inner energy of the liquid are derived using distribution function theory. During the derivation three characters of interaction potential energy of the liquid are assumed. The first is that the interaction force between molecules is the short-range force. The second is that the many-body potential is only relying on the distances between the molecules. The third is that the potential energy of the liquid can be written as the sum of a series of many-body potential . The inner pressure and inner energy can be expressed in the power series of the volume. The coefficients in the series are expressed in many-body potential and radial distribution functions and are only depend on temperature. When onlynth many-body potential is exist, the formula of inner pressure and inner energy are in agreement with the result of perturbation theory obtained by Egelstaff. The results not only give the expressions for parameters but also are suitable for stronger interaction between molecules. Another form of expressions of inner pressure and inner energy is obtained by defining parametersmandα(T). The expressions agreed with the experimental result worked out by Frank. The results give the expressions for parametersmandα(T)and point out that the Frank formulas are tenable only for the liquid which mandα(T)are independent of volume.