[sunnyday]

Hello to everyone!

I've been building an apparatus to compress isothermally butane. It's basically a chamber filled with butane and a piston sliding in.
While compressing i measure temperature with a thermocouple, pressure (pressure sensor) and volume (potentiometer reading piston position).
I can compress butane up to 5 bar (500000 Pa, 70 psi).

Well, the goal was to acquire some data and fit it with both the ideal gas model and the van der Waals state equation.
I did that and altough pressures are not that high, data fitting gives me reasonable van der Waals coefficients (almost close to the values one can find in literature)

So, i've plotted the vdW model and the acquired data.. but i was frightened by the huge difference from the model!!
Here, I've uploaded the plot on my personal website:


http://boccelliengineering.altervista.org/DONE.jpg



What disappoints me is that although the gas seems to behave completely different from the van der Waals model, results of data fitting are nice! Does that mean that van der Waals model is that poor in this region?

This morning the pressure sensor broke up, and changing it would require fabricating a new piston etc, so I cannot test with a "more ideal gas" like pure nitrogen for example..

Thanks a lot for anyone contributing 

[curiouscat]

How did you fit it? A non linear numerical method? Or did you linearize it?

Can you post what coefficients you got? Also, what's your average error?

[curiouscat]

Post your data points too if you can. I'll attempt a fit.

[sunnyday]

Pressure Error and raw data:

the mean pressure error (Pdata - PvanderWaals) is 3.378e+04 Pa, while the standard deviation is 4.308e+04 Pa.

I've uploaded the files here:
http://boccelliengineering.altervista.org/butane/DATA_initial.dat
http://boccelliengineering.altervista.org/butane/DATA_file.dat

The first file contains initial data. I've used it to find the number of moles inside the chamber, assuming at 1bar (≈atm pressure) the butane would behave like an ideal gas:

N_mol = P₀ V₀ / R T₀

then I used this Nmol assuming the chamber is well closed and no butane spills from anywhere. This is confirmed by putting the chamber underwater while in pressure.
Nmol is then required to find molar volume, or to find van der Waals coefficients in dimensional form.

The second file contains the raw data you can see plotted in blue. Volume is in mm3, Temperature in °C, Pressure in Pa.
I expect temperature accuracy to be ± 1°C.

Numerical Method:
I used a very rude method: made a matrix of possible coefficients ranging from a_min to a_max and from b_min to b_max. Then, for every couple (a,b) I computed for every data point the pressure error between measured data and Van Der Waals model with the measured Temperature and volume and summed the square.

i.e. I calculated the mean quadratic error over a wide range of (a,b) values and then picked up those that minimized that error.

Coefficients:
Results:
a = 1.506 Pa m⁶ / mol²
b = 5.36 e-6 m³ / mol
Literature:
a_LIT = 1.389 Pa m⁶ / mol²
b_LIT = 0.0001164 m³ / mol

b coefficient estimation is totally wrong, but I think it's because my pressure and volume range is restricted and also far from critical point

[curiouscat]

Thanks. This helps.

What disappoints me is that although the gas seems to behave completely different from the van der Waals model, results of data fitting are nice!

Umm...Your coefficents especially b are quite off. Dunno if I'd call the fit nice.

Does that mean that van der Waals model is that poor in this region?

Unlikely. More likely you've errors / noise in measurement etc.

[sunnyday]

...ouch..  if only the pressure sensor was ok..
Maybe there's some database where i can find raw data on some gases, to compare with mine?

Also, I was wondering if -assuming the measurements are correct- the fact that my gas is not pure butane could explain the behaviour ( big pressure errors but fitting on "a" coefficient not-that-bad)

Thanks for your interest!!