Calculation of the thermodynamic properties of methane up to $30$ MPa using a new equation of state with regular and scale parts and few constants

The heat capacities $C_v{,}~C_p$ and speed of sound $W$ of methane were calculated by a new equation of state with few adjustable constants. The equation includes a new regular part with $13$ coefficients and a scale part with $6$ coefficients with a regular crossover function containing two fitting parameters. The constants in the equation of state were determined using only $(p{,}~\rho{,}~T)$ data for $\rm CH_4$; no data on $C_v{,}~C_p{,}$ and $W$ were employed, except for the data on isochoric heat capacity $C_v$ in the ideal-gas state and value of $C_v$ at $100$ K on the liquid branch on the liquid–vapor equilibrium curve. The calculated values of $C_v{,}~C_p{,}$ and $W$ are close to the experimental and tabulated values in the regular region. Calculations in the critical region uses universal critical indices $\alpha{,}~\beta{,}~\gamma$ according to the three-dimensional Ising model. A discrepancy with the tabulated data is caused by application of the scaling equation of state. The calculated values are compared with the predictions by the known crossover equations of state for $\rm CH_4$. The root-mean-square error in the description of $\rm CH_4$ pressure is $\sigma_p = 0.5\%$, the mean absolute deviation is $0.3\%$, the uncertainty in $C_v$ does not exceed $5\%$.