How Does Mixing Ideal Gases in a Thermally Insulated Cylinder Affect Pressure?

[Uthpala Kaushalya]

Homework Statement

Consider a rigid piston cylinder arrangement. Assume that the cylinder and the piston are covered by a perfectly insulating material and the piston cylinder interface is very smooth. Two types of ideal gases are separated in the cylinder by the piston. The number of gas molecules of type A is equal to N and the number of gas molecules of type B is twice as that of A. At thermal equilibrium, one finds that the volume occupied by each of gases is the same and equal to V. the temperature of the gas is T, and the temperature of the gas A is twice that of gas B. After a certain time, a door in the piston is slowly opened and the gases are allowed to mix. Find the pressure, after mixing is complete.

Homework Equations

PV = N K_bT

The Attempt at a Solution

 

[physics user1]

Set the equation you wrote with the variables in the final state after the piston was opened

What is the final V?
The final N?
The final T?

 

[Uthpala Kaushalya]

Set the equation you wrote with the variables in the final state after the piston was opened

What is the final V?
The final N?
The final T?

But, isn't there a work done for pushing the piston?

 

[Uthpala Kaushalya]

Set the equation you wrote with the variables in the final state after the piston was opened

What is the final V?
The final N?
The final T?

And how to find the final T ?

 

[physics user1]

Is the same as before

 

[Uthpala Kaushalya]

Is the same as before

The two gases are in two different temperature, aren't they? When applying the equation to the whole system, ( final state ) we need a temperature.

 

[physics user1]

Ahhh, sorry I made a mistake

 

[Chestermiller]

What does this mean: "the temperature of the gas is T, and the temperature of the gas A is twice that of gas B."

 

[Uthpala Kaushalya]

What does this mean: "the temperature of the gas is T, and the temperature of the gas A is twice that of gas B."

Sorry, it should be "Temperature of the gas A is T, and the temperature of the gas A is twice that of gas B"

 

[Chestermiller]

If the outer container is rigid, how much work W does the combined system of two gases do on their surroundings? If the outer container is insulated, how much heat Q gets transferred between the combined system of two gases and their surroundings? From the first law of thermodynamics, what does that tell you about the change in internal energy $\Delta U$ of the combined system of two gases?