Much of the interstellar medium in disk galaxies is in the form of neutral atomic hydrogen, H I. This gas can be in thermal equilibrium at relatively low temperatures, T < 300 K (the cold neutral medium, or CNM) or at temperatures somewhat less than 10^4 K (the warm neutral medium, or WNM). These two phases can coexist over a narrow range of pressures, P_min < P < P_max. We determine P_min and P_max in the plane of the Galaxy as a function of Galactocentric radius R using recent determinations of the gas heating rate and the gas phase abundances of interstellar gas. We provide an analytic approximation for P_min as a function of metallicity, far-ultraviolet radiation field, and the ionization rate of atomic hydrogen. Over most of the disk of the Galaxy, the H I must be in two phases: the weight of the H I in the gravitational potential of the Galaxy is large enough to generate thermal pressures exceeding P_min, so that turbulent pressure fluctuations can produce cold gas that is thermally stable; and the mean density of the H I is too low for the gas to be all CNM. Our models predict the presence of CNM gas to R = 16-18 kpc, somewhat farther than previous estimates. We also examine the potential impact of turbulent heating on our results and provide expressions for the heating rate as a function of Galactic radius.
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