# Pressure-temperature graph without zero y-intercept

1. Jun 25, 2013

### robcowen

I am a high school physics teacher and I've been trying out an experiment for my students. I used a manometer (a plastic tube in a U-shape partially filled with water) to measure the pressure of the air in a boiling tube. I placed the boiling tube into a beaker of water and varied the temperature. I recorded the head difference in mm and converted this to metres.

I used (pressure = density of water x 9.81 x head) to work out the pressure (relative to atmospheric pressure). I then added the local atmospheric pressure (sourced from BBC Weather in millibars and converted to Pa) to the relative pressure to get the absolute pressure of the air.

I plotted a graph of temperature (in Kelvin) against absolute pressure (in Pa) and got a nice straight line relationship. However, my y-intercept should be at zero, according to the ideal gas laws, but is actually crossing at around 90,000 Pa.

Either my gradient is much too shallow (my points are very close to the line of best fit) or I have an absolute error that has shifted my results up the y-axis. The most likely source of this is the atmospheric pressure.

I'm very puzzled and have probably made a silly error somewhere. If you're interested in checking my numbers, please have a look at the attached spreadsheet.

Thanks,

Rob

#### Attached Files:

• ###### Trial results.xlsx
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2. Jun 25, 2013

### Staff: Mentor

Did you use some large gas reservoir in the experiment?
If your gas is in the tube only, the moving water level will change its volume significantly, together with its temperature.

3. Jun 26, 2013

### robcowen

That is something that concerned me, although I would expect a changing volume to cause the line to curve.

The temperature measurement may also be a source of error. I did have a thermometer in the boiling tube, but decided instead to use the one in the water bath. This was because the gas appeared to expand almost immediately (and settle) after the boiling tube was placed in the bath, whereas the thermometer in the boiling tube responded very slowly. This would suggest to me that the rate of heat transfer was much faster through the wall of the boiling tube than it was between the warmed air and the thermometer, so the thermometer in the water bath was more representative of the air temperature than the thermometer in the boiling tube.

4. Jun 26, 2013

### Staff: Mentor

Not significantly, if the volume change is the dominating effect.
Assuming a constant width of the pipe, I get a nice match if the air has a height of 1500mm above your zero-point.

5. Jul 4, 2013

### robcowen

What do you mean by this?

I've done some calculations of the theoretical pressure (pV=nRT) and get a gradient of 346 (as opposed to 42 for the experimental results). I've also built into my calculations an allowance for the change in volume of the air within the manometer - this changes the gradient to 228.

I'm just very perplexed by how far off these results are. I used a boiling tube as the gas reservoir. I've estimated the volume of boiling tube and pipework to be about 64ml, with the changing volume in the manometer being no more than around 3ml. Significant, but it shouldn't dominate.

I've attached my updated calculations (including theoretical pressure) and a photo of the equipment I used.

Any ideas would be greatly appreciated!

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6. Jul 4, 2013

### technician

If the manometer is filled with water then you are not measuring the pressure of air but the pressure of air saturated with water vapour.
You should be using a mercury filled manometer.

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