Boiling Point of Water
Date: 01/29/97 at 09:39:15 From: R. Bruce Radcliff Subject: boiling point of water under pressure Is there an equation that predicts the boiling point of water as the pressure is increased? The research I am doing is in reference to the boiling point of a 50-50 mix of antifreeze and water that is under the pressure of a cooling system of a small gasoline powered engine. I can not find much information on >1 atm. There are copious amounts of information on <1atm. Could you please help? R. Bruce Radcliff
Date: 01/29/97 at 16:06:46 From: Doctor Mitteldorf Subject: Re: boiling point of water under pressure Dear Bruce, Chemistry is messy, and there are few exact formulas. But this is an area where there's an approximate formula from thermodynamics that should help. It works whether the pressure is more or less than 1 atm. The thing I always like to remember is the general rule that the probability of a molecule being in a state of energy E is exp(-E/kT) times a "phase space factor". If you think quantum mechanically, then the space factor tells how many different ways there are for the molecule to be in that state. If you think classically, the phase space factor can be thought of as how much room you have in physical space (x,y,z) times how much room in velocity space (vx,vy,vz). Now, amazingly, this core bit of general knowledge is enough to get us an approximate formula. If the molecules require some energy E to be torn from their cozy home in the liquid and set on their own in the air, then the probability of them being out in the air will be proportional to exp(-E/kT). To the extent that the water vapor behaves like an ideal gas, the pressure is proportional to T times this probability. So: p ~ T exp(-E/kT) (This formula can't be inverted explicitly to give T as a function of p. You have to solve it numerically.) This is a useful formula because E should depend on temperature only weakly. You can treat it approximately as a constant. In theory, E is the heat of vaporization; in practice, you should treat it as an experimental parameter. There's one more free parameter in the system which is the proportionality constant in the expression above. So you should use experimental data to adjust these two parameters for the best fit to the pressure/temperature curve. (All this assumes that the water evaporates, but that the antifreeze component makes a negligible contribution to the pressure.) -Doctor Mitteldorf, The Math Forum Check out our web site! http://mathforum.org/dr.math
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