I Movable Wall in an Adiabatic System: Same Final Temperature?

AI Thread Summary
In an adiabatic container with a movable, heat-conducting wall separating a monatomic and a diatomic ideal gas, the wall's movement leads to a new thermodynamic equilibrium. The final position of the wall can be determined by the thermodynamic properties of the gases, particularly their differing heat capacities, which will result in different final temperatures. Although both gases start at the same temperature and pressure, they will not have the same final temperature due to the nature of their molecular composition. If the gases were real instead of ideal, deviations from the ideal gas behavior could occur, affecting pressure and temperature relationships. The system's initial equilibrium is disrupted by the external force moving the wall, necessitating a new equilibrium state.
Filipeml
Messages
4
Reaction score
0
TL;DR Summary
A monatomic and a diatomic gas, initially at the same temperature and pressure, are separated by a movable, heat-conducting wall in an adiabatic container. How do they reach equilibrium?
Consider an adiabatic container divided into two chambers by a movable, heat-conducting wall. One side contains a monatomic ideal gas, while the other contains a diatomic ideal gas. Initially, both gases are at the same temperature and pressure. Over time, the wall moves until a new thermodynamic equilibrium is reached.

  • How can the final position of the wall be determined based on the thermodynamic properties of the gases?
  • Will the final temperatures of the two gases be the same? If not, what physical principle justifies this difference?
  • If the gases were real instead of ideal, how might the system’s behavior deviate from the predictions of the ideal gas model?
 
Science news on Phys.org
Are some initial p, V, N of the two gases given ?
 
Filipeml said:
. Initially, both gases are at the same temperature and pressure.
Thanks. So I do not think the wall moves.
 
I'm assuming that the wall is forced to move slowly by a rod passing through the wall of the container.

Let n be the total number of moles of the gases in the two chambers and let V be the total volume of the chamber. Let ##\xi## characterize to the fractional volume of the gases in the two chambers (##-1<\xi<+1##), such that $$V_1=0.5(1+\xi)V$$and $$V_2=0.5(1-\xi)V$$so that, at all times, $$V_1+V_2=V$$Let ##\xi_0## be the fractional volumes at the initial state. For an ideal gas, show that, at all times, $$n_1=0.5(1+\xi_0)n$$and $$n_2=0.5(1-\xi_0)n$$
 
Last edited:
  • Like
Likes Philip Koeck and Filipeml
I am amazed that no one in PF has made an attempt to solve this very interesting problem.
 
Chestermiller said:
Estou assumindo que a parede é forçada a se mover lentamente por uma haste que passa pela parede do contêiner.

Seja n o número total de mols dos gases nas duas câmaras e seja V o volume total da câmara. Seja ##\xi## caracterizado pelo volume fracionário dos gases nas duas câmaras (##-1<\xi<+1##), tal que $$V_1=0,5(1+\xi)V$$e $$V_2=0,5(1-\xi)V$$de modo que, em todos os momentos, $$V_1+V_2=V$$Sejam ##\xi_0## os volumes fracionários no estado inicial. Para um gás ideal, mostre que, em todos os momentos, $$n_1=0,5(1+\xi_0)n$$e $$n_2=0,5(1-\xi_0)n$$
Obrigado por sua resposta!
 
Filipeml said:
TL;DR Summary: A monatomic and a diatomic gas, initially at the same temperature and pressure, are separated by a movable, heat-conducting wall in an adiabatic container. How do they reach equilibrium?

Consider an adiabatic container divided into two chambers by a movable, heat-conducting wall. One side contains a monatomic ideal gas, while the other contains a diatomic ideal gas. Initially, both gases are at the same temperature and pressure. Over time, the wall moves until a new thermodynamic equilibrium is reached.

  • How can the final position of the wall be determined based on the thermodynamic properties of the gases?
  • Will the final temperatures of the two gases be the same? If not, what physical principle justifies this difference?
  • If the gases were real instead of ideal, how might the system’s behavior deviate from the predictions of the ideal gas model?
I'm also confused. Why are they not already in equilibrium?
Both gases have the same temperature so there should be no heat transfer through the wall.
Both gases have the same pressure so the wall shouldn't move.
What am I missing?
 
Philip Koeck said:
I'm also confused. Why are they not already in equilibrium?
Both gases have the same temperature so there should be no heat transfer through the wall.
Both gases have the same pressure so the wall shouldn't move.
What am I missing?

As Chestermiller said,
Chestermiller said:
I'm assuming that the wall is forced to move slowly by a rod passing through the wall of the container.

So Question #1 from the op becomes,

Q #1: if you can't see the moving rod, and someone told you the final pressures and temperatures, then could you figure out how much the rod moved?

Q #2 : Would you expect them to report the same temperature for both sides of the container?

Q #3: What if they were real gases? How would things change?
 
Last edited:
  • Like
Likes Philip Koeck
Swamp Thing said:
As Chestermiller said,


So Question #1 from the op becomes,

Q #1: if you can't see the moving rod, and someone told you the final pressures and temperatures, then could you figure out how much the rod moved?

Q #2 : Would you expect them to report the same temperature?

Q #3: What if they were real gases? How would things change?
The problem statement confused me.
The wall doesn't move by itself "until they reach equilibrium".
The system is already in equilibrium and the wall is moved by an external force, so work is done on the system and it moves to a new equilibrium.
 
  • Like
Likes Chestermiller
Back
Top