5 Ideal Gas Law Experiments – PV=nRT and PV=NkT

The ideal gas law may at first seem very abstract but it’s surprisingly easy to demonstrate the the various relationships between the elements. This video gives 5 simple experiments that you can do at home or in the classroom that doesn’t require specialized lab equipment

Since there 5 (or 6) experiments I will break things up accordingly.

  1. Standard latex balloon
  2. Standard latex balloon and an air dusting canister, hair dryer
  3. Air dusting canister
  4. Small empty water bottle or other container, straw, exacto knife, glue gun, cup of water
  5. Oral dosing syringe (can be found in grocery store pharmacy), mini marshmallows
  6. 2 liter plastic bottle, drill, schrader valve, air tight glue (I used E6000), bicycle pump, glass thermometer

Experimental steps:
Again since there 5 (or 6) experiments I will separate them out.

Experiment 0
Not exactly an experiment, but if you simply take a balloon and blow it up it can be represented by the ideal gas law since you are increasing the pressure and volume you must also be adding more molecules of air from your lungs.

Experiment 1
WARNING: Using canned air improperly can lead to frostbite. Please do in a well ventilated area as the gas (difluoroethane) can build up cause asphyxiation.

So in this experiment you will use the canned air improperly, don’t be dumb about it.

  1. Start with a blown up and tied off balloon of whatever size you have handy.
  2. First warm the balloon with a hairdryer. You won’t notice much size change but the larger the temperature change the more drastic the effect so you will get a better result if you do this.
  3. Now holding the air duster canister upside down, squeeze the trigger and let the mist hit the balloon. Turning the balloon to cover all sides. You may want to wear gloves for protection of your fingers while you do this.
  4. After about 30-60 seconds of spraying the balloon should be noticeably smaller.
  5. Take the hair dryer again to restore the balloon to it’s regular size.


Experiment 2
This can actually be carried out in tandem with experiment 1 and works best with air dusting canister. However it can be done with other pressurized containers like: Spot Shot, Whipped Cream, Shaving Cream, Hair Spray. However if you choose to use these other canisters you will end up wasting a lot of the pressurized product.

  1. Hold the pressurized canister in your bare hands and spray.
  2. Spray until you begin to feel the can get cold. This should take about 15 seconds of constant spraying.


Experiment 3

  1. Empty out a small (6-8 oz) water bottle.
  2. Bore a small hole in the cap, just large enough to insert a straw.
  3. Insert a straw through the hole, keeping the long side so it will point out when the cap is replaced.
  4. Glue, with hot glue or other glue, the straw into place. Be sure to make the joint is air tight.
  5. Puth the cap, now with the straw glued in, back onto the small water bottle.
  6. Now cool down your water bottle a little. Either place in a freezer, ice bath or use an upside down air duster.
  7. Then place the straw end into a cup of water and gently hold the water bottle end.
  8. As the warmth from your hands heats the air in the bottle the pressure will increase and many bubbles will come out of the bottom. If you only get a few bubbles make sure you aren’t squeezing and repeat steps 6 and 7. If it still doesn’t work, make sure your bottle, cap and straw is air tight.


Experiment 4

  1. Get a small or large oral dosing syringe and remove the plunger completely.
  2. Put a mini marshmallow into the bottom of the tube.
  3. Reinsert the plunger just a little into the tube again.
  4. Place your finger firmly over the opening opposite the plunger.
  5. Depress the plunger and observe the marshmallow squash down.
  6. Release your finger from the tip for a moment letting the pressure equalize with the surroundings.
  7. Replace your finger, keeping the plunger at the same location.
  8. Now pull the plunger up, while keeping your finger over the hole. Observe the marshmallow puff up.
  9. Enjoy your wrinkly marshmallow.


Experiment 5

  1. Start by drilling a hole into the cap of a standard 2 liter plastic soda bottle. The hole should be large enough to insert a schrader valve (the kind you have on your bike and car tires).
  2. Screw the valve partially in and add glue to the seam. Be sure the glue will dry air tight as it will need to hold a fair amount of pressure.
  3. After the glue is dried place a simple thermometer into the bottle. Be sure you can see the value the thermometer reads from outside the container. You may have to jiggle it around a bit.
  4. Place the cap, now with the valve in place, back onto the bottle.
  5. Write down the value of the thermometer at atmospheric pressure.
  6. Attach the bike pump and begin pumping. Try and find a bike pump with a pressure gauge on it otherwise you risk having your bottle explode.
  7. For best results pump the pressure from 0 to 20psi in as short a time as you can. Look at the thermometer, it should read higher than before the pressure was added. Be careful though if you pump too slowly or wait too long before looking at the thermometer the temperature will begin to drop back to room temperature.


Math: Like I mentioned in the video all of these experiments rely on PV=nRT or PV=NkT. Now you may be wondering exactly what the difference between these two equations is. Simply put little “n” is the number of moles of gas and “R” is the gas constant, while big “N” is the number of actual molecules while “k” is the boltzman constant. However this is mostly just a matter of which units works best for your situation. In these examples you can use either since the main idea is simply that the various elements have to remain balanced.

Experiment 0
This one isn’t that interesting as an experiment goes but even this special case is can be represented by the ideal gas relationship. In the beginning the balloon has a small volume and very few molecules inside the balloon. When I go to blow air into the balloon I add molecules from my lungs, increase the pressure slightly above atmospheric and in response the balloon’s volume increases.

Big P Big V equals Big N little k little t

Note I made both the pressure and volume slightly larger and the number of molecules much larger, this is to represent how each side of the equation changes. Technically there may be a small temperature increase too but it isn’t significant in this example. Similarly since regular air isn’t truly an ideal gas there are some small losses in the rotational energy of the N2 and O2 atoms and vibration and rotational energy in the water and co2 that’s also in the air. But that isn’t really important to the concepts here – that’s entropy stuff, I’ll make another post on that some other time.


Experiment 1
The second experiment also uses the same equation…they all do so I’ll stop repeating that. In any case the What’s happening is that the temperature is decreasing because the pressurized liquid (difluoroethane) is suddenly expanding and evaporating off the surface of the balloon which cools the balloon. Now the temperature inside the balloon is going down and so the equation needs to remain balanced. So either the pressure or the volume must change. Since the balloon is flexible it’s pretty much impossible for the pressure to change so the volume (overall size) has to compensate for the entire balancing act.
P little v equals N K little T

Next when I blow the hair dryer (it’s set on hot) onto the balloon it increases in volume (size) since the temperature increases.

p big V equals N K big T

Experiment 2
When you spray from the pressurized canister the amount of gas inside the canister is going down rapidly. However the volume of the can can’t change since the can is rigid. This means that inside the can the pressure has to be voing doen to keep the equation balanced.

little P V equals N K little T

Now technically there are some number of molecules also leaving the canister. But this is ignored because there are just so many molecules (on the order of 10 ^23)  that even many trillions of molecules moving from one place to another will have little compensating effect, so the overall temperature is what compensates. This is proven out buy the fact that the canister gets cold when you spray from it for a long time.

Experiment 3
This experiment is like the opposite of experiment 2. The idea is that the air inside the small water bottle is at atmospheric pressure and the volume is considered fixed (rigid bottle). Now by the use of body heat you increase the temperature inside the bottle. The only compensating element on the other side of the equation is the pressure, so the air inside the bottle begins to press on the water at the bottom of the straw until it exceeds atmospheric pressure and pushes a bubble out against the water. Again there are some minor losses due to some molecules leaving but the amount of compensation a few molecules provides isn’t enough to keep things balanced…so bubbles.

Big P v equals N K big T

Experiment 4
Now this one is a little different since the two elements that change are on the same side of the equation. Still the basic idea is the same if one element changes something else has to change to keep the overall system balanced. In this case we assume the temperature and number  if molecules is fixed but we have control over the volume via the plunger. So when the plunger is squashed down, while keeping the air inside with your finger the only element that can change (significantly) is the pressure.

Big P little V equals N K T

Now in response to this the tiny bubbles inside the marshmallow that were at atmospheric pressure get squashed by the increased pressure. Next the pressure is equalized (by releasing your finger for a moment) and the plunger is lifted making the volume bigger this time so the pressure has to go down in response.

Little P Big V equals N k T

Now the bubbles inside the marshmallow that were at atmospheric pressure find themselves at higher pressure than their surroundings and expand to balance themselves. Now in truth both of theses examples have the temperature change a little but unless the change is very rapid (like in a fire piston) it’s hard to notice the temperature change.

Experiment 5
The last experiment has a fixed volume, like experiments 2 and 3, except this time we will increase the pressure instead of decrease it or change the temperature. So the thermometer is just to monitor the temperature change and the whole assembly with the valve on the bottle is just to make it easy to change the pressure rapidly. When the pressure goes up fast enough (not adiabatically) the temperature has to compensate.

Big P little V equals N K T

Again there are some more molecules added when the pump is pushed but the have little impact so the temperature has to increase in reaction to the pressure. If the process is done slowly enough the temperature can be kept constant and the number of molecules will then compensate but the change has to be slow. If the change is done fast enough the temperature can increase very quickly, even up to the autoignition temperature of a fuel. This is how a diesel engine works. The piston increases the pressure so much that the change in temperature causes the fuel to light on fire rather than needing a spark from a spark plug to ignite.



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