But for all substances it's true that the heat capacity of the liquid is higher than that for its vapor at the same temperature. K. Mercury is a constant laboratory hazard. Spills must be cleaned up, and that's hard because its high surface tension makes little Hg marbles that roll away from the spill to hide in cracks. Still the slope of that equilibrium line on the phase diagram doesn't become infinite at the critical point. Napoleon's cheap white tin buttons spontaneously changed to gray tin in a Russian winter and fell off, freezing his soldiers.
Gray tin is brittle and crumbles under stress.
Thus did the thermodynamics of phase transitions contribute to modern European history. Napoleon's army retreated, literally in tatters, from Moscow.