Boiling point on top of mount everest

[physstudent1]

Homework Statement

At what temperature does water boil on the top of mount everest, elevation z = 8848m?
Recall that the dependence of pressure with altitude is give by:

P=P_atm * exp(-MWgz/RT)
MW=molecular weight of the gas, P_atm =atmospheric pressure, g is the gravitational acceleration.

Homework Equations

The Attempt at a Solution

Well I have never seen this equation before and I think misusing it is what is throwing me off int his problem. I understand that once I know the pressure of the air on Mt Everest I just need to look through the steam tables and find what Temperature the vapor pressure of water = the pressure of the air. However I am little confused on this equation. What temperature are they looking for? I'm assuming MW would be that of air which I think off hand is like 28g/mol not sure though and R is the gas constant in meters and not sure what other units to use. I also don't really know what to plug in for P_atm because I thought what we were looking for was the atmospheric pressure?! Someone please help this problem should be really easy its only the 6th problem in the first chapter of HW in my thermo book!

 

[mgb_phys]

You use the first equation to get the pressure at the top of Everest
P_atm is the pressure at sea level - the equation is really for a difference in height so if you take z to be measured form sea level that is the pressure you are comparing to.

The variation of boiling point with altitude is a similar equation, rather than retype it - I will just give you the link. http://en.wikipedia.org/wiki/Boiling_point
Interestingly guess which mountain they use as an example!

 

[physstudent1]

what temperature would i put in though 373 K? (normal boiling temp of water?)

 

[physstudent1]

hey I understand to use the equation for pressure but I'm just confused on what Temperature to put into it can anyone help?

 

[mgb_phys]

I don't know where the equation you posted came from but it's not obvious what temperature T refers to.
Do you have a reference for this?

 

[Bacat]

In thermochemistry you need to talk about \Delta_{vap} H, "Enthalpy of Vaporization" instead of boiling point. So once you know the pressure you can use the laws of thermodynamics to calculate how much heat (q) needs to be added to make the water boil. It will be less than 373 K because that is the temperature needed to boil at sea level.

Also, read this quote from the Wikipedia link: "The boiling point corresponds to the temperature at which the vapor pressure of the liquid equals the surrounding environmental pressure."

 

[physstudent1]

its from a problem in my book engineering and chemical thermodynamics by milo koretsky its in a homework problem it just says remember hte equation for pressure based on altitude is : and has it but i have never seen it before.