1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Measuring vacuum w/ hot filament - calculation (pirani gauge)

  1. Jul 14, 2016 #1
    I am looking for guidance on how to successfully measure vacuum using a device similar to a pirani gauge, my device however is a tungsten filament which is heated electrically to about 90*C, and it's current draw is a measure of vacuum.

    The problem I am having is how to relate specifically the current draw to a particular pressure in the system. I know the current draw is inversely-proportional to the resistance, and the resistance varies with the filament temperature, and the temperature varies with gas pressure, warming as the pressure drops due to less thermal conduction and convection.

    Running this in my hobby vacuum setup, it is amazingly sensitive. My particular filament running on 5v reads 46.7 milliamps at 28*C 100kPa, and ~38.1 milliamps as I approach 5pa. But I don't know this minimum pressure yet without an accurate gauge.

    I really need a mathematical model than will tell me the temperature of a tungsten filament given the ambient temperature, power consumption, and pressure. Thanks for any help!

    Here is how the pressure and current relate at higher pressures:

    This test was done with 3.3 volts, vs 5 volts above(corrected).

    ma kPa
    36.17 100
    35.99 86.8
    35.99 76.7
    35.73 60.5
    35.46 47.4
    35.05 34.2
    34.35 21.1
    33.88 7.9
    ~32.2 nearly 0
    Last edited: Jul 14, 2016
  2. jcsd
  3. Jul 15, 2016 #2


    User Avatar
    Gold Member

    @Plat Hi
    If you bought your device, then it should have a calibration chart wrt a certain gas showing the pressure/current curve which is not a straight line but has a few curves in it. It should show operating voltages, and ambient temperature recommendations.

    The filament disipates its heat in a manner of ways. Conduction through the ends of the wire, radiation to the envelope, conduction to the gas, convection to the gas.
    Depending upon the density of the gas in the chamber, or pressure of the gas, the predominate method of heat loss varies.

    With very, very low pressures radiation will predominate, along with conduction along the wire ends.
    As the pressure of the gas increases, direct conduction will begin to predominate.
    With more pressure, convection can begin to be more important, as can the fact that a heat envelope may form around the wire depending upon the mean free path of the gas molecules.

    That's just my thoughts on the subject, if that is what you are after.
  4. Jul 15, 2016 #3
    Thanks for responding, Actually this is completely homebrew, I am using a lightbulb filament that I have mounted inside the vacuum chamber. I was hoping for a way to extrapolate with the current draw known at STP for example, to any lower pressure. Assuming we are below pressures where convection plays a part, would the thermal energy loss due to conduction to surrounding gas be proportional to the density of that gas?
  5. Jul 15, 2016 #4


    User Avatar
    Science Advisor
    Gold Member

    Just calibrate it yourself. Measure the current at a variety of known pressures and construct a calibration curve.
  6. Jul 15, 2016 #5
    I tried doing this as well. I tried using boiling propylene glycol at known temperature to produce a known vapor pressure in the 5-50 Pa range, but I could not get it to boil consistently. I figured this was because of the pressure from he weight of the liquid in a container being too great for the vapor pressure to overcome.

    I then tried saturating a sponge in propylene glycol and inserting a thermometer into the sponge. This cools in the vacuum to a minimum of 11*C, which corresponds to a pressure of 3.4Pa. I find this suspicious because the pump is rated to 5Pa and I know the system isn't perfectly sealed. Do you think this is a valid result?
  7. Jul 16, 2016 #6


    User Avatar
    Science Advisor

    Note that you have some bad data at 76 & 86 kPa, the current is the same.

    Here is the fitted equation for your data:
    y = 34722600 + (4.229631 - 34722600)/(1 + (x/50.38422)^38.66706)

    x = Pirani Current mAmp
    y = Pressure KPa

    Note that the "Y" axis is logarithmic in the graph.

  8. Jul 16, 2016 #7
    Thanks so much, that's just what I needed. I can also add more data points to improve the accuracy. To my question above, when the temperature of the ethylene glycol drops as the pressure is reduced, this is because it is boiling and the pressure in the chamber will be equal to the vapor pressure of ethylene glycol at the particular temperature, correct?
  9. Jul 16, 2016 #8


    User Avatar
    Science Advisor

    The 3.4Pa vs 5Pa I would consider possible, if only because the pump mfg. may have conservatively rated the pump to allow for both degradation during the warranty period and for manufacturing variations.

    As for the "sponge and propylene glycol", I have zero experience with such things and leave it to others to make a reasonable assessment. Sounds like an appropriate and clever approach though! (as long as it doesn't contaminant the vacuum system.)
  10. Jul 16, 2016 #9
    Thanks for your thoughts, I was hoping I had found a reliable way produce very low reference pressures.

    I added the data points for the region below 20Pa and there seems to be a huge change in the graph somewhere between 20Pa and 7.9kPa. At or above 7.9kPa pressure changes very quickly with current draw, and at 20Pa and below, it changes very, very slowly. I'm guessing the transition between cooling largely by conduction and radiation occurs in that gap.
  11. Jul 17, 2016 #10


    User Avatar
    Science Advisor

    OK, I'll speculate. How does the mean free path of the gas compare with the sensor size around 20Pa to 7.9kPa?
  12. Jul 17, 2016 #11
    I suspect the mean free path becomes longer than the filament diameter in the range. I hadn't considered that affect. But I think it is still useful for a sensor because the graph has a one-to-one correlation everywhere.

    Looks like 1.2E-6 meters at 7.9kPa and 4.7E-4 meters or 0.47mm at 20 Pa. That is certainly larger than the filament diameter.
    Last edited: Jul 17, 2016
  13. Jul 17, 2016 #12


    User Avatar
    Science Advisor

    A few thoughts.

    A possible further investigation would be find the breakpoint in the calibration curve then use a much larger sensor and see if the breakpoint moves to a lower pressure.

    To get higher sensitivity, using a thermistor may help. Outgassing may be a problem that could be avoided by purchasing one sealed in a glass probe. That would increase the response time though.

    In any case, since the calibation curve changes shape at lower pressure, you will probably need a higher order formula than mycurvefit.com supplied. There should be other sites that can fit to third or fourth order equations, it's just a matter of finding them.

    Please keep us updated on your results; that way we too can learn. (and it makes us feel good too.:oldsmile:)
  14. Jul 17, 2016 #13

    jim hardy

    User Avatar
    Science Advisor
    Gold Member

    Very interesting..

    I wonder if the thermal element from an automotive mass airflow sensor might work.

    Seconded !
  15. Jul 17, 2016 #14


    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    I vote for splunking down some money and buy an ion gauge and be done with.

  16. Jul 17, 2016 #15
    I found a polynomial regression calculator that can be set to any order here: http://arachnoid.com/polysolve/

    It looks like 3rd order fits best, I don't think higher orders can be right because the function should be continuously increasing, and have no point where the slope is zero. I will test the 600Pa to 7.9kPa range with water of various temperatures and 20Pa to 600Pa with the propylene glycol and fill in that gap.

    Jim, that would be interesting to play with. Sounds good with the hot wire and temperature sensor in one package. Actually never knew how those worked before I searched for it just now.
  17. Jul 17, 2016 #16


    User Avatar
    Gold Member

    I'll have to take your word for the mean free path for ethylene glycol.
    For nitrogen, though it should be something like a meter or so, and 0.0001 m, I think.

    Larger filament diameter will move the bottom flatness of the curve slightly upwards due to more radiation heat transfer.
    It shouldn't affect the loss throught the filament end wires if they stay the same diameter.
    Both radiation and end effects should be fairly constant with change in pressure.

    You want a large enough mean free path so that molecular collisions are minimized. Ideally for the gas conduction to be linear, the molecule should grab the heat from the filament and directly transfer it to the vacuum casing and then come back for more. Collisions are what develops the heat envelope around the filament.
    Colliding molecules exchange energy, so there begins to form a dT/dx around the filament as the mean free path decreases with increased density or pressure.
    At some point gravity puts its nose into the mix, with the resulting bouyancy effect producing convection, and the curve should show an "improved" heat transfer, leveling off again as that effect saturates.

    At the 20Pa you may be hitting the radiation/end effect plateau, and at 7.9kPa the beginning of significant convection currents.
  18. Jul 17, 2016 #17
    Now that you mention it, I completely overlooked the difference in mean free path for ethylene glycol. I just used an online calculator and the molecular diameter of 0.3nm as would be for air. I don't know how to calculate mfp correctly for ethylene glycol. Sorry, I keep confusing ethylene and propylene glycol. I had planned on using propylene and ended up using ethylene instead, having trouble keeping them straight in my head.

    Added another data point at 1.45kPa. Here the curve is becoming very steep and starting to bridge the previously posted graph with the very flat low pressure region.
  19. Jul 17, 2016 #18


    User Avatar
    Science Advisor

    Just out of curiosity I looked for pricing of ion gauges; USD 130 to 650 just for the sensor. The controller/electronics are sold separately. The sensor itself looks moderately simple, perhaps an electronic vacuum tube with its envelope removed could be used. You would still need power supplies of a couple hundred volts, the readout is just a milliamp meter. This could be a project in itself though.

    http://mmrc.caltech.edu/Vacuum/Teledyne Hastings/Ion Gauges.pdf

    When convenient, could you post either you current calibration readings or the curve & fitted equation?
  20. Jul 17, 2016 #19
    I might have to start over and do something different in the way I am creating the reference pressures. Using water, I get significantly different results when I use the sponge vs letting the water boil in a beaker. Even then, the water boils in fits and starts. For some reason, the reading of current draw is much higher when using the sponge, given the water is at the same temperature. I don't understand what could cause this discrepancy. I will be sure to post it up when I think I have good data.

    I'm not sure about the ion gauge, it looks like I would be operating at the very high end of their pressure range and could easily burn the filament. I would love to try an old electron tube if I had a power supply in the 150-200v range.
  21. Jul 18, 2016 #20


    User Avatar
    Science Advisor

    For higher pressures than the heated ion gauges like, there are cold cathode gauges without a filament. The drawback is they need a few kilovolts to operate. If you decide to 'brew your own', a fluorescent lamp ballast is a readily available high voltage transformer (one of the old fashioned magnetic ballasts, not a solid state one.) I'm not really suggesting a cold cathode gauge, just pointing out their existence!

    Commercial vacuum equipment often uses two gauges; one during initial roughing pumpdown, then power on the the low-pressure sensitive ones after a decent vacuum is reached.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted