Merging two chambers of identicle gas

  • Thread starter renlok
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In summary, the question involves two samples of an ideal gas in adjacent chambers, separated by a thermally insulating partition. After the partition is removed and the chambers are merged, the final pressure (Pf) is being asked in terms of the initial volumes (Vx, Vy), pressures (px, py), temperatures (Tx, Ty), and the final temperature (Tf). Using the equation Pv = nRT, the number of moles in each chamber can be calculated as n = PxVx/RTx and n = PyVy/RTy. In the merged chamber, the total number of moles is equal to the sum of n for x and y. Therefore, Tf can be expressed as Pf
  • #1
renlok
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Homework Statement


Two samples of the same ideal gas, x and y, are in adjacent chambers, separated by a thermally insulating partition. The initial volumes, pressures and temperatures of the samples are, Vx, Vy, px, py and Tx, Ty. The partition is removed and the single chamber is brought to a final temperature Tf. If the volume occupied by the partition is negligible, what is the final pressure? (Express your answer in terms of Vx, Vy, px, py and Tx, Ty
and Tf)


Homework Equations


Pv = nRT?


The Attempt at a Solution


I honestly have no idea how to even start this one sorry :/
 
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  • #2
What does n stand for in that equation?
Perhaps you can apply it first to x and y separately and solve for n?
 
  • #3
n is the number of moles in the camber
for x: [tex]n = \frac{P_xV_x}{RT_x}[/tex]
for y: [tex]n = \frac{P_yV_y}{RT_y}[/tex]

for the new camber (merged): [tex]n = \frac{P_yV_y}{RT_y} + \frac{P_xV_x}{RT_x}[/tex]

so [tex]T_f = \frac{P_f(V_x + V_y)}{(\frac{P_yV_y}{RT_y} + \frac{P_xV_x}{RT_x})R}[/tex]

but then i still can't get Tf as i don't know pf (pressure in joined container)
 
  • #4
You are almost there. Please re-read the question carefully. What is your target variable, and which variables should you express it in?
 
  • #5
oh i was trying to find the wrong thing ^^ oh its easy then thankyou
 

What is the purpose of merging two chambers of identical gas?

The purpose of merging two chambers of identical gas is to create a larger volume of gas that is homogeneous in composition. This can be useful in experiments or industrial processes that require a specific gas mixture or concentration.

How do you merge two chambers of identical gas?

To merge two chambers of identical gas, you will need to connect them with a tube or valve system. This will allow the gases to mix and reach equilibrium, resulting in a larger volume of gas with a consistent composition. It is important to ensure that the chambers are sealed tightly to prevent any gas from escaping.

What happens to the pressure and volume when merging two chambers of identical gas?

When merging two chambers of identical gas, the pressure and volume will change according to the ideal gas law. The pressure will increase if the volume decreases, and vice versa. However, the overall number of gas particles and the temperature will remain constant.

Can you merge two chambers of different gases?

Yes, it is possible to merge two chambers of different gases. However, the resulting gas mixture may not be homogeneous and may have different properties from the individual gases. It is important to consider the ideal gas law and the behavior of each gas before merging them.

Are there any safety precautions to take when merging two chambers of identical gas?

Yes, there are a few safety precautions to take when merging two chambers of identical gas. First, make sure the chambers are compatible and can withstand the pressure of the merged gases. Also, ensure that there is proper ventilation and keep flammable or toxic gases away from any potential ignition sources. It is also important to wear protective gear and handle the gases with caution.

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