Fig. 3: Stability and the equation of state.

Analytical results for pressure (p/p_atm) vs. density (ρ/ρ₀) for stable (solid lines) and unstable (dashed lines) equilibria states. The system parameters used are listed below (see caption of Fig. 4). a Comparison between adiabatic (blue lines) and isothermal (orange lines) processes. Dotted lines represent ideal gas. b Examining the effect of v_atm, the volume of the gas encapsulated in a single capsule at atmospheric pressure, and k_II, the slope of phase II. The blue line is a reference curve based on experimental values, with v_atm = 18 ml and k_II = 152 kPa ml⁻¹. The green and purple lines are pressure-density curves for fluid with decreased and increased values of v_atm of 12 ml and 24 ml, respectively. The red line is a pressure-density curve in which one of the unstable permutations is stabilized (see inset), achieved by setting k_II = 2300 kPa ml⁻¹, while keeping all other parameters identical to the blue reference curve. The insets show that decreasing v_atm or increasing k_II creates regions where the fluid is stable although a bi-stable element is at the spinodal region.