Effect of Fluid Expansion on Pressure vessel/chamber

[Tripoly]

Hi,
I have a vessel/chamber filled partially (25%) with silicon fluid (coefficient of thermal expansion is 0.00096 cm^3/cm^3/ °C) and the rest is filled with nitrogen gas at a certain pressure (P1) and temperature (T1).
my question is, how to predict the final pressure (P2) If I increased the temperature to a certain value (T2) ? because I will be having the effect of pressure increase from the gas due to temperature increase and the effect of pressure increase due to vessel/chamber volume reduction occurred by the silicon expansion

 

[anorlunda]

OK, assuming that a negligible amount of the silicon fluid evaporates, and that the silicon oil is incompressible, we can just use the perfect gas law.

Initial : $P_1V_1=n_1RT_1$
Intial quantity of Nitrogen $n_1=\frac{P_1V_1}{RT_1}$
Nitrogen is conserved, so $n_2=n_1$
Volume is conserved so $V_2=V_1$
Final: $P_2V_2=n_2RT_2$

The last step, solving for $P_2$, I leave for you.

 

[jrmichler]

That silicone oil has significant thermal expansion. A 100 deg C temperature change will change the volume of oil by 0.00096 X 100 = 0.096 = 9.6%. Since the oil fills 25% of the volume, the gas space volume change will be about 25% of that, or 0.25 X 9.6% = 2.4% for a 100 deg C temperature change. The pressure change due to volume change is smaller than the pressure change due to gas temperature change, but is still large enough that it needs to be included in the calculation.

I say about 25% because the percent fill changes as the volume of the silicone oil changes.

 

[Tripoly]

OK, assuming that a negligible amount of the silicon fluid evaporates, and that the silicon oil is incompressible, we can just use the perfect gas law.

Initial : $P_1V_1=n_1RT_1$
Intial quantity of Nitrogen $n_1=\frac{P_1V_1}{RT_1}$
Nitrogen is conserved, so $n_2=n_1$
Volume is conserved so $V_2=V_1$
Final: $P_2V_2=n_2RT_2$

The last step, solving for $P_2$, I leave for you.

OK, assuming that a negligible amount of the silicon fluid evaporates, and that the silicon oil is incompressible, we can just use the perfect gas law.

Initial : $P_1V_1=n_1RT_1$
Intial quantity of Nitrogen $n_1=\frac{P_1V_1}{RT_1}$
Nitrogen is conserved, so $n_2=n_1$
Volume is conserved so $V_2=V_1$
Final: $P_2V_2=n_2RT_2$

The last step, solving for $P_2$, I leave for you.

I tried that method to compare it with my experiment. this method is under estimating the results (huge difference) do you think that the Z factor is the reason or what else may affect the results ?

 

[anorlunda]

Might there be moisture in the oil that evaporates to make steam?

I'm not sure what you mean by Z factor.

I'm going to ping an expert @Chestermiller , maybe he can give better help.

 

[Chestermiller]

Might there be moisture in the oil that evaporates to make steam?

I'm not sure what you mean by Z factor.

I'm going to ping an expert @Chestermiller , maybe he can give better help.

The Z factor is the "compressibility factor" which represents deviation from ideal gas behavior. I would guess that the pressures in this system are not high enough for significant deviation from ideal gas behavior. What is the value of P1?

There is another factor that needs to be considered. What is the equilibrium vapor pressure of the oil at the 100 C higher temperature? This will add to the ideal gas pressure of the nitrogen.

 

[Tripoly]

@Chestermiller
experimental results as follows:
initial pressure at 60F is 1,479 psig
finial pressure at 150F is 1,972 psig
Total volume of silicon (occupying 75% of chamber) 240.2 cc
Total volume of the chamber is 320.3 cc
thermal expansion is 0.00096 cm^3/cm^3/ °C
I do not know about the equilibrium vapor pressure but this is the silicon details that I am using
https://krayden.com/technical-data-sheet/dow_510_tds/

 

[Chestermiller]

The absolute pressure ratio is 1.33. The absolute temperature ratio is 1.163. For a 90 F temperature increase, the increase in silicon oil volume is (0.00096)(90)/1.8=0.048 of the initial volume. So, the change in volume of the silicon oil is (240.2)(0.048)=11.5 cc. The initial volume of air is (320.3-240.2)=80.1 cc. So, the volume of air at the higher temperature has decreased to 80.1 - 11.5 = 68.6. So the volume ratio is 0.856. So, assuming Z = 1, the predicted pressure ratio would be 1.163/0.856 = 1.36. This is pretty close to the observed 1.33. What has been neglected here is the increase in volume of the container as a result of thermal expansion.

 

[Tripoly]

The absolute pressure ratio is 1.33. The absolute temperature ratio is 1.163. For a 90 F temperature increase, the increase in silicon oil volume is (0.00096)(90)/1.8=0.048 of the initial volume. So, the change in volume of the silicon oil is (240.2)(0.048)=11.5 cc. The initial volume of air is (320.3-240.2)=80.1 cc. So, the volume of air at the higher temperature has decreased to 80.1 - 11.5 = 68.6. So the volume ratio is 0.856. So, assuming Z = 1, the predicted pressure ratio would be 1.163/0.856 = 1.36. This is pretty close to the observed 1.33. What has been neglected here is the increase in volume of the container as a result of thermal expansion.

Great! many thanks