Why is the Kelvin scale formed using the triple point of water rather than the freezing point? I am trying to learn some thermodynamics by watching the lecture series on YouTube by MIT.
In the second lecture, from 9:00 to 9:45, the lecturer talks about why the freezing point of water as defined in the Celsius temperature scale would make a bad second fixed point (the first being absolute zero), to use to interpolate between and create the Kelvin scale. This is because apparently water doesn't boil at 0 degrees everywhere, it depends on the pressure being 1 atm. He then goes on to say it's better to use the triple point of water instead. This doesn't make sense to me since the triple point of water is only 0.01 degrees at 1atm, just as the freezing point is only 0 degrees at 1 atm.
What is the benefit of using the triple point?
 A: The triple point of water is not found at 1 atmosphere. The triple point exists at a pressure of $661$ Pa, which is a significantly lower pressure, at a temperature of $0.01$ degrees Celsius. If the pressure or the temperature is higher or lower than that, you will never see all three phases of water at once.
If you look at a phase diagram, you can see what is meant here - the freezing "point" is actually a line, a boundary between two phases. In contrast, the triple point is an unambiguous fixed point - the intersection of the boundaries between the three ordinary phases.
As you can see, there are a bunch of other unambiguous fixed points on this phase diagram - one for every intersection of phase boundaries, plus the critical point. The reason the solid-liquid-vapor triple point is preferred over these is because:


*

*It's easier to experimentally create the required temperature and pressure, and

*The experimental signature is very clear: three clearly-different phases exist all at once. This is easier to observe than the transition from gas to supercritical fluid, and it's also probably easier to observe than the simultaneous presence of three different solid phases.



A: If all you know is that water is melting, you don't know the temperature and pressure unambiguously. You can be at any point along water's Fusion Curve. 
If all you know is that all three states of matter are in equilibrium, you know you are at the the triple point designating not an entire curve, but a specific point on multiple curves. 
http://web.mit.edu/10.213/oldpages/f99/diagrams/phase/3phases/index.html

A: Because the triple point of water is NOT set for 1 atmosphere of pressure:

Note how its a diagram of pressure against temperature, and whilst not to scale at all, it does paint a picture.
