I’m having a disagreement with a friend concerning this. He maintains the following:
The temperature of a glass of water filled with crushed ice will vary depending upon your location. Example: This glass of ice water could measure 33 degrees F on the east coast but the same glass may register 34-35 degrees on the west coast due to change in altitude even if the barometric pressure and room temperature are the same.
It seems to me that the temperature of the ice water is a constant at the same surrounding room temperature and barometric pressure and your geographical location has no influence.
One, or perhaps both of us appears to be flirting with the laws of physics or Thermodynamics and I am an expert in neither. Can anyone shed light on this?
Altitude is a complete red herring here. The difference in sea level between the Atlantic and Pacific Oceans is a matter of centimetres, so a glass of water at the East Coast of the US is, to all intents and purposes, at the same altitude as a glass of water at the West Coast.
Of course, if altitude did affect the freezing point of water then in order to change the altitude of a glass of water you wouldn’t have to carry it across the continent; you could just raise it or lower it as desired.
But, as it happens, the freezing point of water does not vary with altitude. The boiling point does, because of lower pressures at altitude, but the same effect is not observed (or only to an infinitismal extent) at freezing point.
Ice melts at the same temperature on the East Coast of the US as on the West Coast. If the volume of the container, the mix of ice and water, the initial temperature of the water added to the glass, the ambient temperature of the environment, etc are the same then the temperature of the mix after a given lapse of time will be the same in both places.
I Googled “water phase diagram” and learned that it does vary with pressure - by a tiny amount. At the pressure equivalent of 120,000 ft altitude, the temperature of an ice-water mixture is about 0.01 degrees C higher than at sea level.
This means that the difference between one location on earth and another is unmeasurably small - even between sea level and the summit of Mt. Everest. The difference attributable to changes in longitude is exactly zero.
But the OP says “even if the barometric pressure and room temperature are the same”, which seems to imply the friend thinks something other than pressure causes the alleged change in melting point with altitude. I could imagine some ridiculously small effects there (like, that the change in g with altitude changes the pressure in the water due to its own density or something), but nothing remotely significant.