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ARQuattr
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I'm trying to determine the internal volume of a container using the ideal gas law principle.
1. A container of known volume is pressurized with air to some known value relative to ambient.
2. The container of unknown volume is vented to ambient.
3. Temperature is constant for all air masses and throughout the experiment.
4. The vent on the container under test is sealed and the containers are allowed to communicate air mass.
5. The final equilibrium pressure of the combined air mass is measured.
6. Determine the unknown volume, given the control volume, initial pressure, final pressure.
Using PV = nRT, I have
PcVc = ncRTc, PuVu = nuRTu, and PfVf = nfRTf, or
nc = PcVc/RTc, nu = PuVu/RTu, and nf = PfVf/RTf
for subscripts c (control container), u (unknown container), and f (final), where
Vf = Vc + Vu, and nf = nc + nu
Then,
PfVf/RTf = PcVc/RTc + PuVu/RTu
and assuming T constant,
PfVf = PcVc + PuVu
Since the unknown container starts at ambient pressure, Pu = 0, so
PfVf = PcVc, or Pf(Vc+Vu) = PcVc
(I've tried this using absolute pressures and it works out the same.)
So the unknown quantity is
Vu = Vc(Pc - Pf)/Pf
Experimentally, this works fine for rigid unknown containers, but when I use a non-rigid container it doesn't. Why not?
By non-rigid, I'm referring to something like a plastic jug with a fairly well-defined volume, but if pressurized, even to only a fraction of a psig, the sides bulge out slightly. This drastically affects the final pressure, but I don't see how. I understand that the volume will increase slightly because of the measurement process, (and I'm able to accept the error in volume measurement due to the expansion of the container,) but the calculation yields a result that is way off.
I can also imagine how the container walls act like springs to increase resistance as it grows, but I don't see how that changes things. The pressure introduced by the control vessel causes the container to expand which allows the pressure to drop until it all reaches equilibrium and my end result should be the final container volume, right?
What am I missing?
Thanks in advance.
1. A container of known volume is pressurized with air to some known value relative to ambient.
2. The container of unknown volume is vented to ambient.
3. Temperature is constant for all air masses and throughout the experiment.
4. The vent on the container under test is sealed and the containers are allowed to communicate air mass.
5. The final equilibrium pressure of the combined air mass is measured.
6. Determine the unknown volume, given the control volume, initial pressure, final pressure.
Using PV = nRT, I have
PcVc = ncRTc, PuVu = nuRTu, and PfVf = nfRTf, or
nc = PcVc/RTc, nu = PuVu/RTu, and nf = PfVf/RTf
for subscripts c (control container), u (unknown container), and f (final), where
Vf = Vc + Vu, and nf = nc + nu
Then,
PfVf/RTf = PcVc/RTc + PuVu/RTu
and assuming T constant,
PfVf = PcVc + PuVu
Since the unknown container starts at ambient pressure, Pu = 0, so
PfVf = PcVc, or Pf(Vc+Vu) = PcVc
(I've tried this using absolute pressures and it works out the same.)
So the unknown quantity is
Vu = Vc(Pc - Pf)/Pf
Experimentally, this works fine for rigid unknown containers, but when I use a non-rigid container it doesn't. Why not?
By non-rigid, I'm referring to something like a plastic jug with a fairly well-defined volume, but if pressurized, even to only a fraction of a psig, the sides bulge out slightly. This drastically affects the final pressure, but I don't see how. I understand that the volume will increase slightly because of the measurement process, (and I'm able to accept the error in volume measurement due to the expansion of the container,) but the calculation yields a result that is way off.
I can also imagine how the container walls act like springs to increase resistance as it grows, but I don't see how that changes things. The pressure introduced by the control vessel causes the container to expand which allows the pressure to drop until it all reaches equilibrium and my end result should be the final container volume, right?
What am I missing?
Thanks in advance.