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The Boiling Temperature of water as a function of pressure

At 100 degrees C, the specific volume of water and steam are 1.043 cm^3/g and 1673 cm^3/g, respectively. The latent heat of vaporization is 2257 J/g.

a) Calculate dP/dT
b) The pressure on the top of the mountain Everest is about 0.35 atm. Calculate the boiling temperature of water at this location.

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First we need to understand why water boils at 100 degrees C when under atmospheric pressure. Liquid water will always evaporate until it reaches equilibrium with water vapor. This happens at a certain partial pressure for the water vapor, the so-called vapor pressure. This evaporation process happens from the water surface. If we were to put the water in a container under some constant temperature T and pressure P, then if P exceeds the vapor pressure for that temperature T, you will have liguid water, if it is below the vapor pressure then all the water will evaporate and you will only have water vapor. Only at P held exactly at the vapor pressure can you have both liquid water and water vapor.

Boiling happens when the atmospheric pressure falls below the vapor pressure. If the atmospheric pressure is above the vapor pressure, then inside the water, you can't have a bubble of water vapor, as such a bubble would be held at atmospheric pressure whuch would exceed the pressure of the vapor in the bubble. When the temperature is such that the vapor pressure exceeds the atmospheric pressure then bubbles of water vapor can form inside the water which the rise to the surface. This is what we call "boiling", this thus starts at that temperature where the vapor pressure becomes equal to the atmospheric pressure. What is important to realize here is that the boiling is a ...

Solution Summary

Detailed explanations and calculations are given. The pressure of the top of the mountain Everest and the boiling temperature of water is determined.