= Solution
At a stated external <pressure>, the <boiling point> of a pure <liquid> is the temperature at which its saturation <vapor pressure> equals that pressure. A vapour bubble inside the liquid must also withstand the hydrostatic head and any <capillary pressure>; the simple free-surface boiling-point rule neglects those small local corrections.
Increasing external <pressure> raises the usual boiling point, while lowering it lowers the boiling point. The <Clapeyron equation> explains the direction:
$$
\frac{dp_{\rm sat}}{dT}=\frac{L}{T\Delta v}>0
$$
for ordinary vaporization with positive <latent heat> $L$ and a larger vapour <specific volume>. Consequently water can boil below its usual open-vessel temperature at altitude or under partial <vacuum>, and above it in a sufficiently pressurized vessel.
Composition also matters. A nonvolatile dissolved solute generally lowers the solvent's vapour pressure and produces <boiling-point elevation> at fixed external <pressure>. A volatile second component can instead raise or lower the boiling temperature according to the mixture's phase equilibrium; an <azeotrope> is a useful warning against applying the nonvolatile-solute rule to every mixture.
Finally, distinguish the equilibrium boiling point from the observed onset of bubbles. A smooth clean vessel or a shortage of nucleation sites can permit <superheating>; agitation or suitable existing sites can make boiling begin nearer equilibrium. Heating power mainly controls the rate of sustained boiling under otherwise fixed conditions, rather than setting an arbitrary new equilibrium boiling point. A thermometer must be placed to measure the intended liquid or saturated vapour region, rather than a locally overheated wall.
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