boiling point - Will the water at the bottom of the tube boil at the same temperature as the water at the top of the tube?

Consider a long, vertical tube of water, as shown below:

Where $P_\mathrm{atm}$ is the atmospheric pressure and $P_\mathrm{bottom}$ is the pressure at the bottom of the tube.

The tube is long enough such that $P_\mathrm{atm}$ is much less than $P_\mathrm{bottom}$.

It is known that water at the surface (top of the tube) will boil at a temperature such that the water's vapor pressure equals $P_\mathrm{atm}$. Let's call this temperature $T$. For example, $T=100~^\circ\mathrm{C}$ when $P_\mathrm{atm}$ is about $1\mathrm~{atm}.

Question: At what temperature will the water at the bottom boil? Will it be higher than $T$ or equal to $T$? Why?

References, if available, would also be greatly appreciated.

Answer

Here's a cool example that should help illustrate the correct answer to your question. As for why it works that way, you might think about it in terms of bubble formation .. in order for a liquid to boil, it needs to form bubbles. Is it harder or easier to do that when the ambient pressure is high?

As for the calculation, you can use the Clausius-Claperyon equation to calculate the correction as described here. You will need some values for $P_0$, $T_0$ and $\Delta H_{vap}$; you can use 1 atm, 373 K and 40.68 kJ/mol.