# Pressure equalization between two tanks

• escape_velocity
In summary, the problem involves two interconnected tanks, A and B, with volumes of 2m^3 and 1m^3 respectively. Tank A contains air at 1 bar absolute pressure and tank B contains air at an unknown pressure. The goal is to determine the initial pressure of tank B that would result in an equalized pressure of 0.8 bar in both tanks after the stopcock is opened. Using the ideal gas law, the number of moles of gas in each tank can be calculated. By setting the initial and final number of moles equal, the initial pressure of tank B can be solved for.
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
Code:
P1V1 = P2V2
be used for solving this problem.
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?

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

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
theodoros.mihos said:
Sing ## P_1,P_2,V_1,V_2 ## before and ##P,V## after mixing and do your calculation again.

DEvens said:
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.

escape_velocity said:
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?

escape_velocity said:
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?

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
DEvens said:
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.

DEvens said:
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 ?

Use ##PV=nRT## by mass conservation.

Chestermiller said:
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

Chestermiller said:
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

Chestermiller said:
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.

Chestermiller said:
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

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

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

Chestermiller said:
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 ??

DEvens said:
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

escape_velocity said:
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

Chestermiller said:
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.

Chestermiller
escape_velocity said:
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

escape_velocity said:
Would it be right to use this
P1 * V1 + P2 * V2 = Ptot * Vtot
Yes. Do you know why?

insightful said:
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

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.

escape_velocity
escape_velocity said:
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

escape_velocity
Chestermiller said:
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?

Raghav Seetharamu said:
How to calculate the approximate time taken to reach the pressure equalibrium?

Chestermiller

## 1. What is pressure equalization between two tanks?

Pressure equalization between two tanks refers to the process of balancing or equalizing the pressure inside two separate tanks. This means that the pressure inside both tanks will be the same, ensuring that there is no significant difference in pressure between them.

## 2. Why is pressure equalization important between two tanks?

Pressure equalization is important because it helps to maintain the structural integrity of the tanks. If there is a significant difference in pressure between the two tanks, it can lead to one tank collapsing or bursting due to the imbalance in pressure. This can also prevent any potential leaks or explosions from occurring.

## 3. How does pressure equalization between two tanks work?

In order for pressure equalization to occur, there needs to be a connection between the two tanks. This can be achieved through a pipe or valve that allows air or gas to flow between the two tanks, equalizing the pressure inside. This connection allows the pressure to equalize until both tanks reach the same level.

## 4. What factors can affect pressure equalization between two tanks?

There are several factors that can affect pressure equalization between two tanks. These include the size and volume of the tanks, the type of gas or fluid inside, the temperature, and any obstructions or restrictions in the connecting pipe or valve.

## 5. How can pressure equalization between two tanks be controlled?

Pressure equalization can be controlled by adjusting the flow of gas or fluid between the two tanks. This can be achieved by regulating the size of the connecting pipe or valve, or by using pressure regulators to monitor and adjust the pressure levels inside the tanks. Additionally, maintaining consistent temperature and removing any obstructions in the connecting system can also help control pressure equalization.

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