What is Pressure?

So what exactly is pressure? I know you think you know what it is - but do you know how it physically manifests itself? Why is there pressure? How do we measure it? What are the units? So many questions and like so many other things in life, it helps to understand the fundamentals of pressure and how it comes to be before you dive in and start doing calculations and the like. So let's get to know pressure.

The BEHAVIOR of Gas Molecules

We need you to THINK about how the molecules behave in a sample of gas. If you can think about it in the right scientific way, you will formulate a model of gas behavior and be able to rationalize all the gas laws. All the mathematical gas laws we have can be developed from simple physical principles. I'd like for you to just learn it and say to yourself "yeah, that makes a lot of sense". If you reach that level of understanding you should congratulate yourself because you've just mastered a rather big scientific theory. That theory is the Kinetic Molecular Theory of Gases. Whoa... that sounds so big and intimidating. Well, it really isn't and one could even say that it is just the details of some "common sense" behaviors that we humans have discovered first hand about gases.

Have you ever played pool? You know, the game with the cue sticks and all the balls on the table with pockets? You can sound even more sophisticated saying billiards. So you start with "the break". On the break you smack the cue ball (the solide white one with no numbers) and send it flying into the set of 15 racked balls. Crack! You hear it! Bam! Impact is made and the balls all go flying off in different directions banging into the bumpers and other balls until eventually the motion stops and it is time for another turn. In physics you learn about conservation of momentum. One ball collides with another and transfers energy to the other while losing energy itself. The momentum is conserved though. Energy lost equals energy gained and now the energy is distributed between the two balls. On the break, all the energy starts out in the cue ball but is soon transferred and distributed to the other 15 balls. So part of this pool ball model is great (energy transfer and motion) - but sadly (for us, not the game), the energy always dissipates in pool and the balls all come to rest. Let's take this idea and run with in for gas molecules.

First, gas molecules can be thought of as tiny-ass little balls in space - aka: molecules. But gas molecules are not bound to just two dimensions of the table top - they get to use all three dimensions in space. They also collide and have perfect transfer of energies thus maintaining conservation of momentum. But here is the big difference - unlike pool balls on a table, gas molecules never run out of the input energy. The molecules just keep on colliding and moving - forever obeying the conservation of momentum and energy that they have. The movement IS the energy. This is known as kinetic energy, the energy of movement. In a physics class you'd learn that any moving obect has a kinetic energy equal to one half times the mass times the velocity squared. Here you go in a real official formula:

\[E_{\rm k} = {1\over 2}mv^2\]

Put your mass in there in kilograms (kg) and the velocity in meters per second (m/s) and you will calculate the kinetic energy in joules (J). Great, but where is this endless energy coming from? For gas molecules, the energy is coming straight from temperature (T). Yes, the absolute temperature (in Kelvin, K) is directly proportional to the kinetic energy of the particles in a sample. If you have a very simple monatomic gas like helium, the kinetic energy in terms of temperature is just:

\[E_{\rm k} = {3\over 2}RT\]

The \(R\) here is the universal gas constant and is 8.314 J/mol K in this case. Notice the units of just joules (J) in the numerator term. So if you double the kelvin temperature, you will double the kinetic energy.

So gas molecules are endlessly banging around into themselves and more so, into the walls of the container they are in. It is the banging into the walls that allows us to model (and correctly think about) pressure. Remember that a moving object (here, a gas molecule) will transfer energy (both outward and inward) when colliding with another object or in this case a wall. The collision delivers a force to the wall and if you add up all the forces from all the molecules in a given area of the wall you have pressure. Pressure is defined as a force distributed over an area. This force per area amounts to pressure as we know it. Some pressure units actually use both those values to describe it. Pounds per square inch, or psi as we know it, is a very popular pressure unit out in the real world. I keep my tires on my car aired up at 35 psi. Or maybe you have a bicycle and keep those tires aired up to 65 psi. Play volleyball? The volleyball should be pumped up to about 4.5 psi. Football? about 13 psi. Basketball? about 8 psi. Just remember, those air molecules inside all those inflatables are zipping around and banging into the walls and creating that pressure.

Now APPLY that Knowledge...

Now lets go through the simple gas law relationships. If you track only volume and pressure of a gas, keeping temperature and moles constant, you'll conclude that if you decrease the volume (you squish the container - push IN the piston) then the pressure will increase. This is an inversely proportional relationship. Makes sense too - if you decrease the volume, you increase the concentration of gas molecules meaning more molecules hit the wall in a given volume than before which means more pressure.

Now lets keep the volume and moles constant and vary the pressure via temperature. Volume is constant if you have a rigid container - or a piston and cylinder locked into position. So think about it. If you increase the temperature, you increase the kinetic energy of all the gas molecules which means they are moving faster. This means they are banging into the walls harder and thus increasing the pressure. That is a law. Increase the temperature increase the pressure. You can also say that pressure is directly proportional to temperature.

If you allow your container to expand and contract you are running a constant pressure and moles experiment and testing volume vs temperature. Increase the temperature and the gas molecules speed up hitting the moveable piston and thus pushing it out until the volume increase matches the temperature increase (by multiplication factors). So volume is directly proportional to temperature.

Finally, lets keep temperature and pressure constant and test out volume vs moles of gas. This is the piston and cylinder where the piston is free to move again. However, we just pump in more gas to change the volume. Double the amount of gas (moles) and you double the volume. Bleed gas out if you want to decrease the volume. You've done this with any inflatable you've ever owned. Pump up an air mattress and you increase the volume by putting in more moles of air. Let the air out and the volume decreases.

How We Measure Pressure

A manometer is a device that measures pressure differences between two regions (sides) of the manometer. The simplest is a U-shaped glass tube that you fill half way with mercury (a very dense liquid). If the left and right sides of the tube have the same pressures, then the liquid levels will match so the difference is zero and the pressure reads "zero". However, you attach a hose with a gas sample on one side and let the other be open to the atmosphere, now you can get a real difference. If your gas is higher in pressure than atmospheric, then the gas side of the manometer will be lower than the open side. Measure the differce in heights of the two sides. If the difference is 91 mm, then your gas is 91 mm MORE than atmospheric. So your relative reading of 91 mm can be changed to absolute pressure by adding the current atmospheric pressure to 91 mm. If the current atmospheric pressure is 753 Torr (same as 753 mm of Hg), then your gas pressure is 753 + 91 or 844 Torr. This converts to 1.11 atm.

You can certainly deep-dive on this in wikipedia. Here is a link to their Pressure Measurement page with lots of info about pressure by difference.

Gauge Pressure A pressure gauge is just a mechanical manometer. This means that a pressure gauge is measuring the difference between your gas sample and the surrounding atmospheric pressure. In general, standard atmospheric pressure is 1 atm, or 760 Torr, or 14.7 psi. So that football you aired up to 14 psi according to your pressure gauge... is really at an actual pressure of 14 + 14.7 which is 28.7 psi inside the ball. Always remember this if you are working gas law problems. The ideal gas law needs the absolute pressure, not gauge pressure. So remember to adjust gauge pressures to absolute by adding the surrounding pressure for that day.

Note: You should generally assume tank and tire and other contained gas pressures are gauge pressures. Most gauges read in "psi" units. Sometimes, to be very verbose, the unit is give as "psig" that "g" on the end stands for gauge. If the pressure is truly absolute (not relative), you have to say "absolute x psi" for your pressure. You can also say the units are "psia" and that "a" on the end stands for absolute pressure. Glad we took care of all that. 😉

A barometer will measure the absolute atmospheric pressure directly. How? Imagine a manometer where one side is a vacuum (zero pressure). If you did that, then your difference in pressure is the same as absolute because it is the difference with zero. How do you built such a thing without using a vacuum pump? Get a 1 meter long glass tube sealed at one end - so this is like a super long test tube. Fill it all the way to the top with mercury (no gaps). Now cover the top and invert the whole thing with the opening pointing down now. Don't spill any mercury. Now plunge the covered end into a resevior of mercury (like a cup of mercury) and remove the cover opening the big tube to the pool of mercury. The mercury level will drop in the tube but stop at the height of atmospheric pressure. It doesn't all run out because there is a vacuum in that empty space at the top of the sealed tube. That empty space is the zero pressure going against the atmospheric pressure that pushes on the mercury surface of the bowl and "pushes" the mercury up the tube until gravity and pressure balance. The height of that mercury column is the ambient atmospheric pressure and should be about 760 mm if you are near sea level - less if you are above sea level.

You can read a lot about barometers on wikipedia. Here's the link to the Mercury Barometer section of that page.

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