How to calculate gas volume released from vessel at drop of press

Hello Technocrats !!!

I have puzzled with some calculation of volume calculation of oxygen and nitrogen gas . In our unit we have three vessels each capacity is 50kL of water, designed press is 36kg. For oxygen storage the two vessels are connected with common header and for nitrogen the single line is connected to the pressure reducing system.
We want to calculate the gas volume released form the vessel. Initially I calculated with with PV=nRT and from another formula but both are not matching.

For example suppose at one instance the total press was 26.5kg/cm2 and after some time it press dropped to 25.5 kg/cm2 then how much volume of gas release. The calculation is as follows-





Oxygen Gas
Change in Mole(P1-P2)*(V/RT)
TTemp in Deg C40Deg C
TTemp in K313Kelvin
P1Press in Kg/Cm226.5kg/cm2
P1Press in Kpa2598.76225kpa
P1Press in N/m22598762.25N/m2
P2Press in Kg/Cm225.5kg/cm2
P2Press in Kpa2500.69575kpa
P2Press in N/m22500695.75N/m2
P1-P2Press Drop98066.5N/m2
RUniveral Gas constant8.314Nm/K Mol
For Oxygen Gas0.2598kJ/kg K
Molar Mass of Oxygen31.99g/Mol
For Nitrogen Gas0.2968kJ/kg K
Molar Mass of Nitrogen28.02g/Mol
VVessel Volume100m3
RT2602.282Nm/Mol
V/RT0.038427811Mol -m2/N
Diff In Mol
(P1-P2)*V/RT3768.480895Mol
1 Mol22.4Liter
Change in Volume (Liter )
Mol X liter84413.97204Liter
1 cubic Meter1000Liter
Change in Volume (M3)84.41397204M3

Another calculation-
Since the volume capacity of the vessel is 50kL at 36 kg/cm2
Then gas volume when press was 26.5 kg/cm2 press = 50 x1000x26.5/1000
V1=
1325​
m3
Then gas volume when press was 25.5 kg/cm2 press = 50x1000x25.5/1000
V2=
1275​
m3
Gas Volume released =V1-V250m3
Since both vessels are joint with common header hence the total volume releases
= 2x (V1-V2)
=100 m3

I want to know which calculation is correct
 
Mani15...

Your approach seems rather hectic, so, let's start with basics:

Step 1) Before you consider any change of condition(s), what are the total moles of each gas at the temperature and pressure conditions you cited?

Step 2) Will be given once you have presented the answer to Step 1 !

Regards, Phil Corso
 
Mani15....
Your "Ideal Gas Law" Formula is incorrectly applied !
For a simpler approach I suggest you search this Forum's Archives for Gi.Fi.E.S. pronounced "Jiffys".
 
Mani15...

Your approach seems rather hectic, so, let's start with basics:

Step 1) Before you consider any change of condition(s), what are the total moles of each gas at the temperature and pressure conditions you cited?

Step 2) Will be given once you have presented the answer to Step 1 !

Regards, Phil Corso
Ok Sir
Can you please correct me .

I want to calculate the gas volume released from the vessel with help of press drop.

My volume capacity of the tank is 50kL of water and the max allowed press is 36kg/cm2 . Normally we fill the gas (N2) up to 32 kg/cm2 . Now we utilized the gas for our process after some time the press dropped to 28Kg/cm2 after 1hr 36 min. them how much valve of nitrogen gas we utilised.
The vessel is under open air environment and the ambient temp is max 40 degree in side gas temp is 35 degree.
No filling is going on during the utilization of the gas.

Thanks in advance
 
Mani15...
For your 1st calculation... the "Ideal Gas Law" calculation:
a) You used the wrong units for "P" and "V".
b) The two O2 tanks should be treated as one tank.
c) "N" should be "n",
d) The equation should have been PV = nRT.
e) "N" is used in the equation PV = NkT.
f) Time of pressure decrease had nothing to do with problem, just added confusion.
g) Finally, you paid no attention to "rounding-up" the final answers.
Had you done the simple equation I asked you to do, your error would have become clear !

Phil Corso
 
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