

Boiling Point versus Altitude Equation
Name: Nelson
Status: student
Grade: 912
Country: Brazil
Date: Fall 2011
Question:
What is the equation relating the boiling point of water with altitude on Earth? (without the variable "pressure"). At sea level, the boiling point of water (100% H2O) is 100 degrees Celsius. This everybody knows... :D I am saying in generic terms, say, altitude h, in meters (sea level: h = 0). Whenever possible, please justify where the "magic numbers" (physical constants) are. This way these constants will mean something.
Replies:
Nelson,
You will need to find an equation that relates altitude to
atmospheric pressure. And then relate the atmospheric pressure to
boiling point.
For the second task, there is an equation called the
ClausiusClapeyron equation which relates the boiling point of any
liquid based on two variables, the external pressure and the
enthalpy of vaporization. Since enthalpy is a function of the
substance, it is essentially something that can be analyzed or
looked up in a table. The external pressure becomes the only variable factor.
Greg (Roberto Gregorius)
Canisius College
Nelson,
It is a good question. I have just worked something out by
hand, but since I have not seen it elsewhere I wonder if
I have done it right or not. Still here it is, working from
two famous formulas (in my case I pulled them
from Atkins and DePaula's Physical Chemistry text).
By combining the barometric formula with the Clausius Clapeyron
equation and assuming that the atmospheric pressure at
sea level is 1 atm, I get the boiling point T_B at height h
as being given approximately by the following reciprocal
formula:
(1/T_B) = (1/T_B^*) + (ah/T_a)
where T_a is the ambient temperature, i.e, the temperature of
the room (this determines the atmospheric pressure);
T_B^* is the boiling point at 1 atm pressure; and
a = (Mg/enth), where M is the average molar mass of air (about 29 g/mole),
g is the gravitational contant, and "enth" is the enthalpy of
vaporization of water (about 44 kJ/mole I believe). All units
must be converted to SI in order for this formula to work at all.
Note that if h=0, the boiling point equals T_B^*, and also
that if h > 0, the boiling point is less than T_B^*, as expected.
Also, if the ambient temperature is cold that will lower the
boiling point as well (because it decreases the ambient pressure).
This formula is highly approximate. The CC equation is sometimes only
good to two significant figures, etc etc. However, it does seem
to capture the essentials.
Thanks for the great question!
best, Dr. Topper
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Update: June 2012

