Pressure equalization between two tanks

[escape_velocity]

Homework Statement

Given 2 tanks A and B.
Tank A has a volume of 2m³ and contains air at pressure 1 bar absolute
Tank B has a volume of 1m³ and contains air.
Tank A and B and interconnect with a pipe and has a stopcock and is currently closed.
What is the pressure or air that would be needed in Tank B such that after the stopcock is opened and pressures in both tanks have equalized the pressure in both tanks now is 0.8 bar.

Homework Equations

Can the equation

P1V1 = P2V2

be used for solving this problem.
I'm a bit wary about this since boyles law applies to a

fixed amount of gas

since this problem involves 2 cyclinders can we consider the gas to be

a fixed amount

The Attempt at a Solution

P1 = ?
V1 = 1m³
P2 = 0.8bar
V2 = 2 + 1 = 3m³

P1 = (0.8 * 3) / 1
P1 = 2.4bar
Which seems to be incorrect, intuitively I would have said that the pressure in the smaller tank (tank B) should have been below 1 bar to get the equalization pressure to 0.8 bar.
Where am I going wrong?

 

[theodoros.mihos]

Sing $P_1,P_2,V_1,V_2$ before and $P,V$ after mixing and do your calculation again.

 

[DEvens]

Maybe you will solve the problem easier if you imagine that there is a very thin plastic sheet between the two volumes of gas such that they do not mix after you open the valve. So the two quantities of gas will change their volumes until the pressure equalizes. At that point they will each have the same 0.8 bar of pressure.

Or, to put it another way, you have two fixed amounts of gas, each of which obeys the equation you mention.

p1 v1 = p2 v2
p3 v3 = p4 v4

You know the before volumes for each, the before pressure for one, and the after pressure for each.

 

[escape_velocity]

Sing $P_1,P_2,V_1,V_2$ before and $P,V$ after mixing and do your calculation again.

p1 v1 = p2 v2
p3 v3 = p4 v4

You know the before volumes for each, the before pressure for one, and the after pressure for each.

For the first amount of gas in TankA
P1=1bar
V1 = 2m³
P2 = 0.8bar
V2 = 3m³ ??
For the second amount of gas in TankB
P3 = ?
V3 = 1m³
P4 = 0.8bar
V4 = 3m³ ??
Now that's where I get stuck.

 

[DEvens]

For the first amount of gas in TankA
P1=1bar
V1 = 2m³
P2 = 0.8bar
V2 = 3m³ ??

$3 m^3$ is the volume for both quantities. What is the volume for the original quantity that was at 1 bar and now is at 0.8 bar?

For the second amount of gas in TankB
P3 = ?
V3 = 1m³
P4 = 0.8bar
V4 = 3m³ ??
Now that's where I get stuck.

Again, $3 m^3$ is the volume for both. The other quantity got calculated above. So what is V4? And so then what is P3?

 

[Chestermiller]

Apparently, you are are supposed to assume that the temperature does not change (as would be the case for an ideal gases with no heat entering or leaving and now work being done on the surroundings). Let the temperature be T. In terms of T and the gas constant R, how many moles of gas are there in tank A to start with? In terms of T, R, and the initial pressure P of tank B, how many moles of gas are there in tank B to start with? In terms of these parameters, how many moles of gas are in both tanks to start with? In terms of T and R, how many moles of gas are present in 3 cubic meters of gas at 0.8 bars? Set the initial total number of moles equal to the final number of moles, and you will have your equation for determining P.

Chet

 

[escape_velocity]

3m33 m^3 is the volume for both quantities. What is the volume for the original quantity that was at 1 bar and now is at 0.8 bar?

For Tank A The tank volume would be constant at 2m³ but air volume would increase since pressure has dropped by 20% the volume would increase by 20% and that would be 2.4 m³.

Again, 3m33 m^3 is the volume for both. The other quantity got calculated above. So what is V4? And so then what is P3?

For tank B we know tank volume 1m³ and final Pressure 0.8bar if there was 1 bar abs in the beginning again at 0.8 bar pressure the volume would go up by 20% and it should be 1.2m³.
But can I assume this 1bar as initial pressure of tank B ?

 

[theodoros.mihos]

Use $PV=nRT$ by mass conservation.

 

[escape_velocity]

In terms of T and the gas constant R, how many moles of gas are there in tank A to start with?

PV = nRT
P = 1bar
V = 2 m³
R = 8.3144621 * 10^-5 m3.bar/K. mol
T = 27 deg. C = 273 + 27 = 300 deg K
n = PV/RT = 2/(8.3 * 10^-5) * 300
n = 200000/2490
n = 80.3 moles

In terms of T, R, and the initial pressure P of tank B, how many moles of gas are there in tank B to start wit

I do not know the initial pressure of tank B

In terms of these parameters, how many moles of gas are in both tanks to start with?

Again initial pressure of tank B is unknown.

In terms of T and R, how many moles of gas are present in 3 cubic meters of gas at 0.8 bars

n = 96.22 moles

Set the initial total number of moles equal to the final number of moles, and you will have your equation for determining P.

 

[Chestermiller]

You know that there are 80.3 moles in tank A to start, and 96.22 moles in tanks A and B combined. So how many moles are in tank B to start? So you know the number of moles in tank B to start, and you know the temperature and volume of tank B. So, what is the initial pressure in tank B?

Chet

 

[escape_velocity]

You know that there are 80.3 moles in tank A to start, and 96.22 moles in tanks A and B combined. So how many moles are in tank B to start?

Is it possible to find moles without knowing the initial pressure??
If The total moles of gas inside the 2 cylinders will be constant through out the experiment...
Then the moles in tank B would be 96.22 - 80.3 = 15.92
but this seems to be quite low compared to tank A which was 80.3 ??

 

[escape_velocity]

Maybe you will solve the problem easier if you imagine that there is a very thin plastic sheet between the two volumes of gas such that they do not mix after you open the valve. So the two quantities of gas will change their volumes until the pressure equalizes. At that point they will each have the same 0.8 bar of pressure.

Would it be right to use this
P1 * V1 + P2 * V2 = Ptot * Vtot

 

[Chestermiller]

Is it possible to find moles without knowing the initial pressure??
If The total moles of gas inside the 2 cylinders will be constant through out the experiment...
Then the moles in tank B would be 96.22 - 80.3 = 15.92
but this seems to be quite low compared to tank A which was 80.3 ??

Not really. The pressure is going to be lower and the volume is only half.

So, now that that is settled, what is the original pressure in tank B?

Chet

 

[escape_velocity]

So, now that that is settled, what is the original pressure in tank B?

PV = nRT
P = ?
V = 1 m3
R = 8.3144621 * 10-5 m3.bar/K. mol
T = 27 deg. C = 273 + 27 = 300 deg K
n = 15.92 moles
P = nRT / V
P = 0.4 bar

So 0.4 bar of pressure would be needed in Tank B to get the final equalization pressure of 0.8 bar in both tanks.

 

[escape_velocity]

So 0.4 bar of pressure would be needed in Tank B to get the final equalization pressure of 0.8 bar in both tanks.

Having said that why couldn't we just use

P1 * V1 + P2 * V2 = Ptot * Vtot

 

[insightful]

Would it be right to use this
P1 * V1 + P2 * V2 = Ptot * Vtot

Yes. Do you know why?

 

[escape_velocity]

Yes. Do you know why?

For Tank A and Tank B, P*V = constant
so when we connect Tank A and Tank B that becomes say a large Tank C so after equalization the PV of this tank will also be constant
so we can say
P1 * V1 + P2 * V2 = Ptot * Vtot

 

[insightful]

Well, I start with n = PV/(RT) and n(initial) = n(final). Then, when I write the conservation of moles equation, RT cancels on both sides. In other words, PV is constant because n (and hence nRT) is constant. There are different approaches that work; just so you're comfortable with yours.

 

[Chestermiller]

Having said that why couldn't we just use

P1 * V1 + P2 * V2 = Ptot * Vtot

This is OK, if you understand fundamentally what it is saying.

If you divide this equation by RT, then you end up with the mole balance that that I was discussing in my posts, and that Insightful was referring to. Both of us felt that using the mole balance was an easier way of understanding what's happening. In any event, it is always very worthwhile for a student to examine two different approaches to the same problem (if two approaches exist).

Chet

 

[Raghav Seetharamu]

This is OK, if you understand fundamentally what it is saying.

If you divide this equation by RT, then you end up with the mole balance that that I was discussing in my posts, and that Insightful was referring to. Both of us felt that using the mole balance was an easier way of understanding what's happening. In any event, it is always very worthwhile for a student to examine two different approaches to the same problem (if two approaches exist).

Chet

How to calculate the approximate time taken to reach the pressure equalibrium?

 

[DrClaude]

How to calculate the approximate time taken to reach the pressure equalibrium?

Please open a new thread with your question instead of adding it to an existing (and old) thread.

Thread closed.