Receiver Pressure Equalizations Calculations

[vapl153]

I have a question about pressure equalization. I have 2 receiver thermically insulated (adiabatic) and connected via a valve, one receiver 10 cu/ft at 100 psig and 350 F, the other receiver is 1 cu/ft at 0 psig and 60 F. using n=1.406, what would be the equalizing pressure and temperature when I open the valve ? (the valve and piping not to be considered in the calculation).

Is this ok ?

P1= 100 psig = 114.7 psia
V1= 10 cu/ft
T2 350 F = 810 abs

P2= 0 psig = 14.7 psia
V2= 1 cu/ft
T2= 60 F = 520 abs

The combining result
P3= ?
V3= V1 + V2
T3= ?

PV= P1V1 + P2V2 = 1147 + 14.7
PV= 1161.7
PV/T= P1V1/T1 + p2v2/t2 = 1.416 + 0.02826
PV/T= 1.4443
PV/T = P3V3/T3

P3 = PV / V3 = 1.4443/11 cu/ft
P3 = 105.6 psia = 90.91 psig
T3 = (PV/T) / PV = 1.4443 / 1161.7
T3 = 804.32 abs = 344.32 F

I don't know how to solve it with n, receiver 1 in expansion and receiver 2 in compression,

Thanks, Dan

 

[Achy47]

Dear Dan, thank you for your question about pressure equalization. Your calculations seem to be correct. The equalizing pressure would be 105.6 psia or 90.91 psig, and the equalizing temperature would be 804.32 abs or 344.32 F. However, I would like to clarify a few things about your question and calculations.

Firstly, the value of n=1.406 you mentioned is the heat capacity ratio for air at constant pressure and constant volume, not the polytropic index. The polytropic index would depend on the process and cannot be determined with the given information.

Secondly, I assume that the receiver 1 is in expansion and receiver 2 is in compression because of the difference in pressure and temperature. If this is not the case, please provide more information about the process.

Lastly, I would like to mention that your calculations do not take into account the effects of the valve and piping. While they may not have a significant impact on the result, they should be considered in a more accurate analysis.

I hope this helps clarify your question. Please let me know if you have any further questions or if I can assist you with any other scientific inquiries. Best of luck with your research!



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