pressure - Explanation for different boiling points of water on different altitudes

I understand water boils at different temperatures depending on altitude.

I am seeking to get an illustrative explanation for this, including a diagram if possible.

Answer

Boiling point of water changes with altitude because atmospheric pressure changes with altitude.

So, how/why boiling point changes with pressure.There is good explanation of this at hyperphysics (with diagrams).

Now, why does pressure change with altitude? Imagine you are swimming in water. Deeper you go more pressure you feel, because there is more water above you.

$P = P_0 + \rho gh$

$P$ - pressure, $P_0$- pressure at the surface, $\rho$ - density of fluid, $g$ - gravity of Earth, $h$ - height/depth to free surface

There is huge column of air above our heads.

$\rightarrow h$ at sea level > $h$ at hill station.

$\rightarrow P$ at sea level > $P$ at hill station.

$\rightarrow$ boiling point at seal level > boiling point at hill station.