MadSci Network: Physics

Re: What squashed the plastic bottle - vacuum or air pressure

Date: Mon Apr 21 18:58:58 2003
Posted By: Michael Weibel, Test and Evaluation Project Manager (applied chemistry)
Area of science: Physics
ID: 1050483854.Ph

Good question!

To answer it, let's start with an understanding of what pressure and 
vacuum are.  Pressure is the force (push) exerted by air molecules 
bouncing off of things.  The pressure exerted by a gas contained within a 
fixed volume can be approximated by the Ideal Gas Law:  PV=nRT   

where:  P = pressure of the gas
        V = volume of the gas
        n = # of moles of gas (basically, the # of gas molecules)
        R = the Ideal Gas Constant
        T = absolute temperature of the gas

(you can find usage of this equation in any college level general 
chemistry textbook, which can usually be found at the library)

Basically, if you reduce the amount of gas in a fixed volume (lower the 
n), or drop the temperature, the pressure drops (see the equation).

At sea level and 0 degrees Centigrade (32F), atmospheric pressure is 14.7 
pounds per square inch (psi).  Consequently, the pressure drops as you 
increase in altitude (less air molecules at hgher altitude) or decrease in 

Now, we're ready for a definition of vacuum...very easy:  the absence of a 

When you boil water in a 2L bottle, you're turning liquid water into water 
vapor (gas), which displaces the air in the bottle.  At this point, the 
pressure in the bottle is slightly higher than that outside the bottle, so 
if anything, the bottle may bulge a little.  When you seal and cool the 
bottle, the water vapor condenses, leaving behind a (partial) vacuum (much less gas 
inside the bottle than outside).  Remember that atmospheric 
pressure "pushes" with 14.7 psi.  Inside the bottle, the pressure is 
probably 2-3 psi, so the bottle experiences a push (squeeze) of about 12 
psi.  A 2L bottle probably has about 50 square inches of surface area (try 
calculating it!), so you're exerting a net force of about 600 lbs!!!!  
this is why the bottle squishes.  

(the only force is that of the collisions of the gas molecules, not the 
imagined "sucking" of air)

Hope this answers your question (and tells you who had it right).


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