Discovering Gas Compressibility: 8th Grade Science Fair Project

[Mach15]

Hello everyone. We are working on a 8th grade science fair project. We are trrying to conduct experiments that will let us find the relationship of a particular gas's compressabilty and its temerature increase when compressed. We are trying to make the project reletivly advanced, and hope to be able to use physics formulas to enhance our experiments and our results. We are planning to compress the gas by pumping the gas into a compression chamber. The chamber will have a measurement "probes" with which we will measure the temperature and pressure of the gas inside when compressed. We are wondering how you find the compressibilty of a particular gas with the compression design that we have decribed. We asume that compressabilty of a gas is the compression rate and the work being done. In order to find that out we need to know the amount of substance (moles) we will be compressing. We have found the ideal gas law PV=nRT and we are wondering if we can use this formula to find the amount of substance we are compressing. If anyone can help don't hesitate to reply.

Thank You

 

[berkeman]

Yep, that's exactly what you use. Here's a starting resource to learn more:

http://en.wikipedia.org/wiki/Ideal_gas_law

 

[Dale]

You might also want to look at the hyperphysics site:

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idgcon.html#c1

 

[Mach15]

Thank you for the replies.

Greetings. Initially, thanks guys.
It's good to know that we are on the right track. We have seen hyperphysics before its a great site. It took us a long time to figure out what a mole was, so we will look over hyperphysics and if we do have (which we probably will) any more things that need to be cleared up we will ask here. Does anyone see any problems with the design of our project?

 

[FredGarvin]

The compressibility of a gas is a very specific thing with a well known definition:

$$Z=\frac{p \overline{v}}{\overline{R}T}$$

where:

$$Z$$ is the compressibility factor

$$p$$ is pressure

$$\overline{v}$$ is the specific volume, i.e. $$\frac{m^3}{kmol}$$

$$\overline{R}$$ is the universal gas constant

There are thermodynamic texts that have charts showing the variation of compressibility versus pressure at specific temperatures. A more general chart which applies to many gases is the generalized compressibility chart which is reliant on terms known as the reduced pressure and reduced temperature. This chart is much more useful in that it is not specific to the gas you are using. The following link shows the exact charts I have in a couple of my thermo texts:

http://higheredbcs.wiley.com/legacy/college/kaminski/0471268739/addtl_content/ch05.pdf

You may want to do some research and find the ones for the gases you are experimenting with to see just how accurate your results are. Good luck!

 

[Q_Goest]

Hi Mach

We are planning to compress the gas by pumping the gas into a compression chamber. The chamber will have a measurement "probes" with which we will measure the temperature and pressure of the gas inside when compressed. We are wondering how you find the compressibilty of a particular gas with the compression design that we have decribed. We asume that compressabilty of a gas is the compression rate and the work being done.

The term “compressibility of a gas” regards how a gas deviates from ideal behavior. FredGarvin provided the equation that indicates how to calculate the factor, Z (also called the “compressibility factor”). Note this is a dimensionless factor which tells you how much a real gas deviates from ideal gas behavior. It doesn’t tell you anything about the thermodynamics of the gas. For air at low pressure (ie: less than a few hundred psi) and close to atmospheric temperature, the compressibility factor of air is going to be so close to 1 that you probably won’t be able to measure it accurately. All this is saying is that air can be considered an ideal gas under the conditions one might expect a lab experiment like yours to operate under.

You mention “work being done” and that you want to measure temperature and pressure. This seems to indicate that you’re not looking for the compressibilty factor however. Seems like you’re thinking that as the gas goes into this pressure vessel, you’re expecting to measure some kind of increase in temperature that will correlate to pressure rise. Is that right? If so, then there’s a whole lot more to doing something like this and actually getting real numbers than simply putting a gas into a vessel.

Per the first law of thermo, what you’re doing is simply adding a gas to a vessel such that the increase in internal energy is equal to the enthalpy coming in. Neglecting heat transfer, the equation reduces to:
dU = Hin
where dU = change in internal energy
Hin = the enthalpy of the air going in

This is different than compressing a gas using a cylinder. In that case, the work being done on the air is going directly into increasing the internal energy. Neglecting heat transfer, the equation for this reduces to:
dU = Win
where
Win = work put into compressing the air = Force times distance = Pressure times area times distance.

You can measure work fairly accurately to find dU in the case of a cylinder. For the case where you’re simply pumping air into a vessel however, Hin is an unknown and dU is an unknown so you really can’t determine those values from a simple experiment like this. Seems to me, you should be considering doing the experiment in which you’re actually compressing a gas in a cylinder with a sealed piston.

Another problem with either experiment is you don’t know the heat transfer, which will be significant. So even calculating dU and determining temperature rise with pressure, the end result will be skewed due to heat transfer.

Maybe the simplest way is to use the polytropic formula. Look about ¾ of the way down this page for the heading “Polytropic Compression”:
http://www.cbu.edu/~rprice/lectures/compress.html

You’ll find an equation used to relate temperature and pressure, which is the 3’rd equation under the heading. Temperature is in absolute (ie: Rankin or Kelvin) and pressure is also absolute, not gage pressure. The exponent n should be 1 for a case where there is so much heat transfer that the air stays at constant temperature, and 1.4 for a case where there is no heat transfer at all. The real case of compressing air in a cylinder by applying a piston and doing work on the air will be somewhere in between because there will be some heat transfer, but not isothermal conditions.

Hopefully that gets you started in thinking about what your experiment should look like and what you might measure.

 

[Mach15]

Hello

Q_goest,
Thanks for your reply and your advice. You guessed our science fair project research question correctly, the research question is (It can be changed if neccessary) "What is the relationship between the compressability of a particular gas and it's temperature increase when comressed?" We were initially going to use the "piston" design to make our compressor, but because of gass leaking through the edges of the piston, and the simplicity and seemingly additional accuracy of the "adding gas" model, we abandoned the "piston" model. I have seen the polytropic formula on a different site before, but did not understand it. Will the "addding gas" model be applicable with the polytropic formula? We are greatly interested in using it to enhance our Sci Fair Project.

FredGarvin,
Thank you for your compressability factor formula. I have written it down and hopefully we will be able to use it in our project.

 

[Q_Goest]

Ok, that’s kinda what I thought you had in mind.

The reason the first method of simply adding gas to a cylinder (dU = Hin) is different than the latter is because of a few things. The gas is assumed to mix inside the cylinder, and the gas coming in is generally assumed to have a specific temperature (slightly above atmospheric). The end result is a temperature in the vessel which doesn’t increase along a line of constant entropy, the temperature is always much lower. However, in some cases such as very long tubes, the gas that starts out in the tube, is mostly pushed to the far end by the incoming gas resulting in very little mixing. This results in a much higher temperature at the far end of the tube, away from the inlet since no mixing can occur. In fact, if NO mixing occurs to this initial slug of gas that’s in the tube, the temperature can increase very closely along a line of constant entropy. In the case of oxygen systems for example, Teflon lined hoses and carbon steel pipe have been seen to burn since this added heat in a pure oxygen environment results in sufficient heat to initiate a fire, so non-flammable materials must be used.

The reason I’m explaining all this is because I’d like to suggest that this principal of preventing any kind of mixing with the incoming gas be used to try and obtain a temperature rise that closely follows a line of constant entropy, which will be the highest possible temperature rise. Also, you can then use the polytropic equation using n (the exponent) equal to the ratio of specific heats (n = 1.4) and show how the polytropic equation can be used to predict temperature rise.

Another post I was commenting on https://www.physicsforums.com/showthread.php?t=212009", was interesting because of the suggestion of putting a balloon into an atmosphere and expanding or compressing it that way. Using a balloon means there’s no exchange of that initial slug of air with the air that’s coming in. Also, the balloon has very little thermal mass and a low conductive heat transfer coefficient. The heat transfer in such a balloon would be primarily dictated by convection between the air and the balloon, both inside and outside the balloon. In other words, heat transfer will be minimized by doing this. That’s a good thing!

I attached a sketch of what I’m thinking of. Basically, put a thermocouple or thermister into a balloon and inflate it, sealing it around the temperature probe wire. Then put the balloon, fully inflated, inside a pressure vessel or perhaps a piece of pipe with capped ends. Cap everything. When you’re ready, pressurize the pipe using an air source and measure the temperature inside the balloon. It should increase rapidly, and roughly follow the polytropic equation for n=1.4. What will prevent the temperature from rising along a line of constant entropy will be heat transfer. Both the balloon skin and the thermal mass of your measuring device will contribute significantly to heat transfer, so best to make your balloon initially as large as possible to increase the air’s mass, meaning your pipe must be big, and your thermocouple has to be as small as possible. Also suggest measuring the pressure inside the balloon before the experiment starts since it will be above atmospheric. Also, take into consideration the absolute pressure where you are. Denver for example is something like 12 to 13 psia (going from memory) so high altitude will also affect this. The absolute pressure in the balloon is what you want to put into the equation.

Oh, and the more rapid the pressure increase, the less time there is for heat transfer and the closer the temperature will rise along a line of constant entropy.

If you wanted to, you could have kids design different experiments playing with the different variables (ie: have different themocouples, fill the balloon more or less, pressurize faster or slower, etc….) and see what causes the highest possible temperature.

If you need materials, I’d suggest McMaster Carr or Grainger for small bits like this. Even if you can’t scrounge the parts, the total cost for brand new stuff shouldn’t exceed a few hundred $.
http://www.mcmaster.com/
http://www.grainger.com/Grainger/wwg/start.shtml

 

[Dale]

We were initially going to use the "piston" design to make our compressor, but because of gass leaking through the edges of the piston, and the simplicity and seemingly additional accuracy of the "adding gas" model, we abandoned the "piston" model.

You can put your gas inside a ball or other bladder. That would solve the leakage problem. It may make determining the volume change more difficult.

EDIT: I should have read Q_Goest's comments first. Similar idea for leakage, but he really thought about the whole setup.

 

[Mach15]

Ok, that’s kinda what I thought you had in mind.

The reason the first method of simply adding gas to a cylinder (dU = Hin) is different than the latter is because of a few things. The gas is assumed to mix inside the cylinder, and the gas coming in is generally assumed to have a specific temperature (slightly above atmospheric). The end result is a temperature in the vessel which doesn’t increase along a line of constant entropy, the temperature is always much lower. However, in some cases such as very long tubes, the gas that starts out in the tube, is mostly pushed to the far end by the incoming gas resulting in very little mixing. This results in a much higher temperature at the far end of the tube, away from the inlet since no mixing can occur. In fact, if NO mixing occurs to this initial slug of gas that’s in the tube, the temperature can increase very closely along a line of constant entropy. In the case of oxygen systems for example, Teflon lined hoses and carbon steel pipe have been seen to burn since this added heat in a pure oxygen environment results in sufficient heat to initiate a fire, so non-flammable materials must be used.

The reason I’m explaining all this is because I’d like to suggest that this principal of preventing any kind of mixing with the incoming gas be used to try and obtain a temperature rise that closely follows a line of constant entropy, which will be the highest possible temperature rise. Also, you can then use the polytropic equation using n (the exponent) equal to the ratio of specific heats (n = 1.4) and show how the polytropic equation can be used to predict temperature rise.

Another post I was commenting on https://www.physicsforums.com/showthread.php?t=212009", was interesting because of the suggestion of putting a balloon into an atmosphere and expanding or compressing it that way. Using a balloon means there’s no exchange of that initial slug of air with the air that’s coming in. Also, the balloon has very little thermal mass and a low conductive heat transfer coefficient. The heat transfer in such a balloon would be primarily dictated by convection between the air and the balloon, both inside and outside the balloon. In other words, heat transfer will be minimized by doing this. That’s a good thing!

I attached a sketch of what I’m thinking of. Basically, put a thermocouple or thermister into a balloon and inflate it, sealing it around the temperature probe wire. Then put the balloon, fully inflated, inside a pressure vessel or perhaps a piece of pipe with capped ends. Cap everything. When you’re ready, pressurize the pipe using an air source and measure the temperature inside the balloon. It should increase rapidly, and roughly follow the polytropic equation for n=1.4. What will prevent the temperature from rising along a line of constant entropy will be heat transfer. Both the balloon skin and the thermal mass of your measuring device will contribute significantly to heat transfer, so best to make your balloon initially as large as possible to increase the air’s mass, meaning your pipe must be big, and your thermocouple has to be as small as possible. Also suggest measuring the pressure inside the balloon before the experiment starts since it will be above atmospheric. Also, take into consideration the absolute pressure where you are. Denver for example is something like 12 to 13 psia (going from memory) so high altitude will also affect this. The absolute pressure in the balloon is what you want to put into the equation.

Oh, and the more rapid the pressure increase, the less time there is for heat transfer and the closer the temperature will rise along a line of constant entropy.

If you wanted to, you could have kids design different experiments playing with the different variables (ie: have different themocouples, fill the balloon more or less, pressurize faster or slower, etc….) and see what causes the highest possible temperature.

If you need materials, I’d suggest McMaster Carr or Grainger for small bits like this. Even if you can’t scrounge the parts, the total cost for brand new stuff shouldn’t exceed a few hundred $.
http://www.mcmaster.com/
http://www.grainger.com/Grainger/wwg/start.shtml

Thanks very much for the reply and the design.
I think we will use your design for our science fair project. I have a few questions though. I looked at the Polytropic equation,do you think you could explain to me some things about it. First of all, P1 and P2, what two pressure values are these? T1 and T2 for temperature? Wpoly? Do we just substitute 1.4 for n or do we find it from suction and discharge conditions? Or, what is the ratio of specific heats to substitute in for n? I'm sorry I do not know very much.

We plan to get tanks of Nitrogen, Oxygen, Helium, CO2 and whatever different gas we can get a hold of to do the compression experiment on. So when you speak of pressurizing the pipe with air, do we just pump the particular gas in like we planned to in our original "adding gas" model? If so, where does the pressure gauge go in the "balloon" model? We live at sea level and a really small city, so I the atmospheric pressure would be "standard"?

I forgot to tell you, this probably doesn't change anything, but just in case. In our "adding gas" model we planned to insert a nozzle to the cylinder so when we started to pump gas into the cylinder we could let small amounts of mixture of the gas we want to compress and normal air escape, wait till it purifies. Then seal the cylinder, and continue pumping the gas into let it compress. We have an Ace hardware nearby that sells PVC and such Tubes, will that be able to supply us? The "balloon" model seems like a great idea and makes me hopefull of our project!

 

[Q_Goest]

I looked at the Polytropic equation,do you think you could explain to me some things about it. First of all, P1 and P2, what two pressure values are these? T1 and T2 for temperature?

P is absolute pressure (ex: psia) and T is absolute temperature (ex: degrees Rankin). 1 is for the initial or first state and 2 is for the final or second state. If you measure the initial pressure and temperature, then pressurize the experiment and take the final pressure and temperature, you should find that, given some exponent, the polytropic formula predicts this final state. So if you solve the polytropic formula for T2 for example, you should be able to verify that the temperature you calculate matches the temperature of the formula. Alternatively, you could solve for n.

Do we just substitute 1.4 for n or do we find it from suction and discharge conditions? Or, what is the ratio of specific heats to substitute in for n?

This is the tricky part. You can’t know exactly what the exponent is because you can’t determine exactly how much heat will flow out of the relatively hot balloon and into the gas that you’re using to pressurize with. Also, heat flows into the balloon skin and also into the thermometer, so there are other locations where heat can be lost. The experiment provided is intended to minimize the amount of heat transfer, and hopefully come close to adiabatic conditions (ie: no heat transfer).

The value of n however, can be anything between 1 and k where k=ratio of specific heats. For the case where you have a lot of heat transfer, or a lot of time such that the final temperature equals the initial temperature (process is isothermal), then the exponent n is 1. The more heat transfer, the closer to 1 you’ll get. For the case where there is no heat transfer, the exponent is equal to k. So if you minimize heat transfer, you should get the maximum value for n which is simply k.

We plan to get tanks of Nitrogen, Oxygen, Helium, CO2 and whatever different gas we can get a hold of to do the compression experiment on.

Please don’t use oxygen. Everything becomes much more flammable in a pure oxygen atmosphere, and you’re very likely to blow something up. Similarly, don’t use a flammable gas like hydrogen. What you want to use is nitogen (k=1.4), helium (k=1.67) and CO2 (k=1.3 (aprox) – deviates from ideal gas as pressure increases).

I assume you’re going to be obtaining high pressure (~ 2200 psig) gas from cylinders. Yikes! Are you familiar with what safety precautions you need?

So when you speak of pressurizing the pipe with air, do we just pump the particular gas in like we planned to in our original "adding gas" model?

I’d suggest just using up to 100 psig air from a compressor so you don’t overpressurize anything. If you’re using high pressure cylinders, you might explode something. Just fill the balloons with gas (from your cylinder) and use compressed air at 100 psig to pressurize your pipe or tank.

Regarding balloon pressure, you can measure air pressure (cylinder pressure) and make the assumption that the balloon is at the same pressure. You might want to correct for this by checking to see what pressure the balloon creates when you blow it up. It will probably vary a bit depending on the dimensions. The larger you blow it up, the higher the pressure will be.

Regarding PVC, I wouldn’t suggest using it for this experiment. Can you afford a steel pipe nipple? (threaded on both ends). I think we should talk about what you want to use for this to ensure the apparatus is safe.

 

[Mach15]

Hello. Yes we need to talk about the safety of the project. So, oxygen and hydrogen are out then. Yes we plan to use high pressure the cylinders you describe, unless our local industrial gas supplier stores gas differently. It is not so much that we can't afford something, it is that we are under reasonable time pressure, and probably can't wait for one week priority mail. From what I know PVC has very high strength, is it not strong enough to have 100 Psi of gas pressure? Also, won't we need to be drilling holes into our cylinder for pressure gauge? Also, with the polytropic equation's predictions, should the temperature that our temperature probe would be reading increase almost immediatly, or will it increase at a steady rate? Should we subtract the absolute pressure in the balloon in our equation? Any input would be of much help.
Thank You

 

[Q_Goest]

Here's my suggestion...

Hi Mach,
You can get compressed gas from your local industrial gas supplier. Use that gas to fill up the balloons only. Don’t use it for the cylinder. Explain to your supplier what you’re doing and they should be able to give you balloon filling devices that can screw into the cylinder valve. The Compressed Gas Association (CGA) requires different types of fittings for different types of gasses, so you may need more than 1 balloon filling device. The cylinder valves have different outlets. I don’t have the CGA book handy, but the supplier can give you details.

Also, instead of helium, you might want to consider argon which as the same ratio of specific heats (1.67) and might be cheaper or easier to obtain.

PVC can take a pressure of 100 psig or even more, but using it to contain a gas is dangerous. Most places that sell it will even tell you it isn’t good for gas. Besides which, you’ll be using it in a circumstance where it will get hot which means it can loose much of it’s strength. Use steel instead. You can get the following pieces from McMaster Carr. They usually send them overnight for a small fee.
Pipe nipple, threaded, 6” sched 40, 8” long: 44615K185 ($62.44 ea)
Pipe caps, 6”, threaded: 44605K536 ($139.15 ea)
or
Pipe Nipple, threaded, 4” sched 40, 8” long: 44615K135 ($20.94 ea)
Pipe cap, 4”, threaded: 44605K392 ($28.12 ea)

The 6” pipe is much more expensive than 4”, but it would offer quite a bit more volume. That’s up to you.

Next, you need an air tank. You can get one that looks like this from Walmart, K-Mart, or automotive parts stores: http://www.northerntool.com/webapp/wcs/stores/servlet/product_6970_200319119_200319119

This one has a small valve on it and a hose. The hose is ¼” ID. If you charge up the tank with air and connect this tank to a fitting on your cylinder made of pipe, you can pressurize it very quickly and safely. You’ll need a fitting from a hardware store or McMaster Carr:
Barbed tube fitting, ¼” ID tube to ¼” Pipe Thread: 44555K132 ($2.12)
Put a stainless hose clamp on it to keep it there.

A compressor can be purchased at Walmart or K-Mart also. They’re cheap, around $20.

The pipe caps need to be drilled and tapped for a ¼” pipe thread. You might try going to a local machine shop and asking them to drill and thread the cap for you. They may even do it for free. Show them the fitting so they know what to do. If you need to, you can always drill and tap the thread yourself. It’s not that tough really. The local hardware store can sell you the drill and pipe tap.
You also need a pressure gage and be able to mount this. Get a T fitting and screw it into the cap, then thread the barbed fitting into the T on one side and a pressure gage to the other. More McMaster Carr parts:
The T Part Number: 50785K222 ($3.05)
Pressure Gage Part Number: 3846K6 ($7.24) Specify 0 – 160 psig range.
Use Teflon tape on all male pipe threads. Obtain from hardware store.

As for the thermocouple, I’ll leave that up to you. I’m assuming you already have something in mind for it.

I also attached a spreadsheet to do this calculation. Good luck.

 

[Mach15]

Q_Goest,
Thank you very much. We have started experimenting already. Since we couldn't afford buying the pipes online we instead bought 2 inch Diameter Galvinized pipe, and got caps and sealent on both ends. One cap has a "T" connecter, which in one side we screw in a pressure gauge and one side we plug in a bike pump. For balloons we got those long kinds that people tie up and make dogs out of. Our local industrial gas supplier has donated us the gas and let us borrow the cylinders and balloon fillers. We have good results, there is an approximatly 10 degree C increase with 100 psi of pressure, and I can pump the cylinder to 100 psi in about 37 seconds. So the process is not exactly adiabetic or isentropic. Can't we calculate heat transfer to find the approximate value of n in the polytropic formula? (http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/heatra.html#c2 where k of latex is approximately 0.16) How can we do this?