A review of existing works on the determining the adiabatic index was carried out. Various methods are considered for determining the adiabatic index of an ideal and real gas for methane at the temperatures of 100–600 K and the pressures of 1–1000 bar, with a mass fraction of the vapor phase q > 0.6. In the specified range, heat maps were constructed on the temperature-entropy (T-S) diagram for adiabatic indices obtained from the relationships proposed by V.A. Istomin. (canonical adiabatic exponent from differential relations), A.M. Shekhtman. (adiabatic indicator based on the differential ratio of the product of density and compressibility coefficient), and on the ratio of isobaric and isochoric heat capacities as a function of real gas parameters. An analysis of the errors of various equations for isentropic expansion of a gas (the equation of isentropic expansion of an ideal gas, an equation taking into account the compressibility coefficient z, an equation using canonical adiabatic exponents) was carried out relative to the equation of state for a real gas in the form of a fundamental equation, explicit with respect to the Helmholtz free energy. A new equation for calculating the exhaust with canonical adiabatic exponents is obtained, and a new method for deriving the classical exhaust equation, based on iterative mixing of a gas isentropically expanded in a vessel and isenthalpicly expanded to ambient pressure, is proposed. Based on this conclusion, an iterative method for calculating the exhaust process is described, which allows obtaining results in any area, including two-phase one, taking into account the real properties of the gas. Exhaust lines were plotted on T-S diagrams in the pressure ranges of 50-1 bar and temperatures of 100-600 K. A comparison of various exhaust calculation methods is carried out, and the features and disadvantages of previously existing methods near the two-phase region are described.