An Alternate View of Condensation

Usually when we think of condensation, we think of the droplets of water that form on a cold glass on a humid day, or perhaps we think of dew making the grass wet on a summer morning, or maybe the fog that forms on the bathroom mirror after you have a hot shower.  In those familiar cases of condensation, the water vapor is mixed in with dry air in a very dilute mixture.  For example, at 75 deg F, 60% relative humidity, the water vapor comprises only about 1.1% of the total moist air, by mass.  Even at 75 deg F, 100% relative humidity, (at which point the vapor is about to start condensing to liquid) the water vapor is only about 1.8% of the mixture.  So, we’re accustomed to condensation of water from a very dilute mixture of water vapor in air.  In this blog, we’ll consider the condensation of pure water vapor, and see some surprising forces.
We know that at 1 atm (14.7 psi), water boils at about 212 deg F.  Water vapor and liquid water will exist in equilibrium at that temperature and pressure.  We can think of that temperature-pressure pair in two ways.  In one view, it is the temperature at which liquid water will start to boil if we hold it at 1 atm and raise the temperature from some lower value.  Conversely, it is also the pressure at which 212 deg F liquid water will start to boil if we were to lower the pressure from some value higher than 1 atm.
The pressure at which 75 deg F water will start to boil is 0.43 psi. Again, this temperature-pressure pair is where the vapor and liquid will exist in equilibrium.  So, if we maintained liquid water at 75 deg F, and imposed a lower pressure than 0.43 psi, some of the water would boil into vapor until the pressure equilibrated at 0.43 psi.  Or, if we held some water vapor at 75 deg F and imposed a higher pressure than 0.43 psi, some of the vapor would condense until 0.43 psi was reached.
Now, imagine that you had a sealed container completely filled with water vapor at 1 atm (and 212 deg F). What would happen if the container and enclosed water vapor were both cooled to 75 deg F? 
As the container cooled, the water vapor would start to condense to liquid water.  Eventually, if the container were strong enough to remain rigid, the water would reach a new equilibrium between the condensing vapor and the condensed liquid with a pressure of 0.43 psi.  Of course, the container would be under considerable stress at that point, because every point on the surface would have a net pressure of 14.7 psi – 0.43 psi = 14.3 psi.  So, for example, if your container were a cube six inches on a side, the force on each side of the cube would be 514 lb.  A tank with steel plate walls could easily support that kind of force, but many thin walled containers would simply collapse from the outside atmospheric pressure pushing in on the low-pressure interior.
In order to illustrate this, I filled a milk carton with steam at atmospheric pressure.  Then, I put the milk carton under a cold water tap in the sink.  As expected, the thin-walled plastic milk carton couldn’t support the atmospheric pressure as the steam inside condensed, and the milk carton got crushed.  This movie shows the process. 

This picture shows the final state of the milk carton.  

[If you estimate the forces on the sides of the carton, you’ll wonder why it wasn’t crushed even flatter.  That is because there was still a little bit of air inside, even though I did my best to get most of it flushed out and replaced by steam before I cooled it.]