arXiv subjects
Publications and source records attributed to Ikhtier H. Umirzakov.
The closed-form expression for the quantum partition function of the improved Tietz oscillator is obtained using the Voronoi summation formula.
It is shown that the existence of single critical point of the fluid described by van der Waals equation of state is not the hypothesis and it is the consequence of the thermodynamic conditions of liquid-vapor phase equilibrium. It is also shown that the thermodynamic conditions of liquid-vapor phase equilibrium of the fluid give equalities to zero of first and second partial derivatives at constant temperature of pressure with respect to volume at critical point which are usual conditions of existence of critical point.
It is shown that the proof of [1] that the specific heat of the system of classical point particles interacting with each other via uniform gravitational potential energy may be negative is incorrect.
It is shown that there is no proof of negativity of specific heat of the system placed in thermostat. It is proved that for the system of particles placed in the thermostat and interacting with each other via uniform potential energy the total energy is linear function of the temperature so the isobaric heat capacity is constant along the line of the zero pressure if the latter exists and the isobaric heat capacity is negative for value of the degree of uniformity of the potential energy negative and more than -2 and it is non-negative if otherwise.
The paper analyzes a general case of an equation of state, which is an analytical function at the critical point of the liquid-vapor first order phase transition of pure substance. It is shown that the equality to zero of the first- and second-order partial derivatives of pressure with respect to volume (density) at the critical point is the consequence of the thermodynamic conditions of phase equilibrium. We obtained the relations of critical exponents and amplitudes with parameters of the analytical equation of state. It is shown that the substance with the analytical equation of state can have critical exponents of lattice gas which is equivalent to the two dimensional Ising model. It is shown that the analytical equation of state can take into account the density fluctuations.