# Homework Help: Thermodynamics: box with a moving wall

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1. Dec 7, 2017

### Das apashanka

• Moved from a technical forum, so homework template missing
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+31/γ)γP/2
D.(31/γ/1+31/γ)γP
I have a doubt regarding option c as in the denominator I m getting 2ϒ
I want to clarify whether I m right

2. Dec 7, 2017

### stockzahn

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

3. Dec 7, 2017

4. Dec 7, 2017

### Das apashanka

3PVϒ=pV1ϒ
PVϒ=pV2ϒ
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

5. Dec 7, 2017

### Staff: Mentor

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?

6. Dec 7, 2017

### Das apashanka

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

7. Dec 7, 2017

### Staff: Mentor

What is the EXACT statement of the problem?

8. Dec 7, 2017

### Staff: Mentor

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?

9. Dec 7, 2017

### Das apashanka

it is allowed to move freely and the wall is insulated

10. Dec 7, 2017

### Staff: Mentor

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

11. Dec 7, 2017

### Das apashanka

ok thank you

12. Dec 7, 2017

### Staff: Mentor

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.

13. Dec 7, 2017

### Das apashanka

thanks it helps me in clearing the concept