Thermodynamics: box with a moving wall

[Das apashanka]

I have a doubt regarding the answer, a box separated by a movable wall has two compartments filled by a monotonic gas .Initially the volumes are equal but the pressure are 3P and P respectively .When the wall is allowed to move the final pressure is
a.(2/3)^γP
b.3(2/3)^γP
C.(1+3^1/γ)^γP/2
D.(3^1/γ/1+3^1/γ)^γP
I have a doubt regarding option c as in the denominator I m getting 2^ϒ
I want to clarify whether I m right

 

[stockzahn]

I think you are right, I also obtain 2^γ.

 

[DrClaude]

Please show your work.

 

[Das apashanka]

3PV^ϒ=pV₁^ϒ
PV^ϒ=pV₂^ϒ
and V₁+V₂=2V
Where p=final state pressure and V₁ and V₂ are final state volume of the two boxes,V is the initial state volume
Solving the above three the result comes

 

[Chestermiller]

The equations you are attempting to use are valid strictly to the case of an adiabatic reversible expansion and/or compression. If the wall is allowed to move with no constraint, the process will not be reversible, and the equations will not apply. Only if, during the process, the motion of the wall is controlled externally in very gradual increments will it be possible to carry out the process reversibly.

What is the exact statement of the problem?

 

[Das apashanka]

The equations you are attempting to use are valid strictly to the case of an adiabatic reversible expansion and/or compression. If the wall is allowed to move with no constraint, the process will not be reversible, and the equations will not apply. Only if, during the process, the motion of the wall is controlled externally in very gradual increments will it be possible to carry out the process reversibly.

What is the exact statement of the problem?

the four options are given and only one is right,using the arguments given previous I obtained option c with an amendment I want to clarify whether I have done right and what will be the correct option

 

[Chestermiller]

the four options are given and only one is right,using the arguments given previous I obtained option c with an amendment I want to clarify whether I have done right and what will be the correct option

What is the EXACT statement of the problem?

 

[Chestermiller]

Is the wall force to move gradually (so that the volume changes of the gases are reversible) or is it allowed to move freely (unconstrained)? Is the wall insulated (so that no heat can flow from one side to the other), or is it conductive of heat?

 

[Das apashanka]

Is the wall force to move gradually (so that the volume changes of the gases are reversible) or is it allowed to move freely (unconstrained)? Is the wall insulated (so that no heat can flow from one side to the other), or is it conductive of heat?

it is allowed to move freely and the wall is insulated

 

[Chestermiller]

it is allowed to move freely and the wall is insulated

If this is the case, then none of the answers is correct.

 

[Das apashanka]

If this is the case, then none of the answers is correct.

ok thank you

 

[Chestermiller]

ok thank you

If the wall is forced to move gradually (not freely) and the wall is insulated, then the correct answer is C, if the 2 in the denominator is corrected to be $2^{\gamma}$. If the wall is allowed to move freely and is not insulated, the final pressure is 2P.

It is also possible to approximate the solution to this problem if the wall is insulated and allowed to move freely if we assume that, on both sides of the wall, the pressure throughout the process is constant and equal to the final value of the pressure.

 

[Das apashanka]

If the wall is forced to move gradually (not freely) and the wall is insulated, then the correct answer is C, if the 2 in the denominator is corrected to be $2^{\gamma}$. If the wall is allowed to move freely and is not insulated, the final pressure is 2P.

It is also possible to approximate the solution to this problem if the wall is insulated and allowed to move freely if we assume that, on both sides of the wall, the pressure throughout the process is constant and equal to the final value of the pressure.

thanks it helps me in clearing the concept