calculation of thermodynamic properties of the quasi-one dimensional liquid 3he at finite temperature

we have used a variational approach to calculate some thermodynamic properties of the quasi-one dimensional liquid 3he such as the energy, entropy, free energy, equation of state and heat capacity at finite temperature. we have employed the lennard-jones potential as the inter-atomic interaction. we have seen that the total energy increases by increasing both temperature and density. as expected, it is seen that the entropy decreases by increasing density and decreasing temperature. there is no minimum point in the free energy curve, showing that there is not any bond state for the quasi-one dimensional liquid 3he. the results of our calculations indicate that the equation of state of this system becomes stiffer as the temperature increases. our results for the specific heat show that there is not any lambda transition for this system.