Entropy Change of Ideal Gas Upon Inserting Wall

In summary, the conversation discusses the Gibbs paradox and how the insertion of a wall in an isolated gas system leads to a decrease in multiplicity and entropy. However, it is mentioned that the decrease in entropy may be small compared to the scale of the system's entropy and it is unclear which degrees of freedom are lost when the wall is inserted. Overall, there is a decrease in entropy when a moving wall is pushed inwards and the degrees of freedom disappear, but the extent of this decrease is subjective.
  • #1
AcidRainLiTE
90
2
To preface my question, I know it is related to the Gibbs paradox, but I've read the wikipedia page on it and am still confused about how to resolve the question in the particular form I state below.

Suppose a completely isolated ideal gas consisting of identical particles is confined to a volume V. Call this state 1.

Now insert a wall dividing the volume in half, so that you now have two completely isolated system, one with N1 particles one with N2 particles. Call this state 2.

Regardless of how the inserted wall partitions the particles, the multiplicity of the system in state 2 will always be less than the multiplicity of the system in state 1 because state 1 includes every configuration compatible with state 2 (i.e. configurations with N1 particles on one side and N2 on the other) as well as additional configurations (configurations with N1 + 1 on one side and N2 -1 on the other, etc).

Hence, the entropy of the system always decreases upon insertion of a wall.

I understand that the decrease may be small compared to scale of the system's entropy, but small or not, does the system's entropy decrease in this example?
 
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  • #2
I guess the same subjectivity of entropy that is mentioned in wikipedia is relevant in this case too.

The system loses some degrees of freedom when the wall is inserted, but we don't know which ones, so there is no decrease of entropy.

In such case where the volume decreases when a moving wall is pushed inwards, we know which degrees of freedom disappear, so in this case there is a decrease of entropy related to the decrease of degrees of freedom.
 

1. What is entropy change of an ideal gas upon inserting wall?

The entropy change of an ideal gas upon inserting wall refers to the change in disorder or randomness of the gas molecules when a wall is inserted in the container. This is a thermodynamic process that can be calculated using the formula ΔS = q/T, where q is the heat added or removed and T is the temperature in Kelvin.

2. How does inserting a wall affect the entropy of an ideal gas?

Inserting a wall in a container of ideal gas increases the entropy of the gas. This is because the gas molecules are confined to a smaller space, leading to an increase in disorder and randomness. This is reflected in the increase in the value of entropy calculated using the formula ΔS = q/T.

3. Does the number of gas molecules affect the entropy change upon inserting a wall?

Yes, the number of gas molecules does affect the entropy change upon inserting a wall. As the number of gas molecules increases, there is a greater chance for collisions and interactions between molecules, resulting in a higher entropy change. This is because more molecules will be affected by the insertion of the wall, leading to a greater increase in disorder and randomness.

4. How does temperature affect the entropy change of an ideal gas upon inserting wall?

Temperature has a direct relationship with the entropy change of an ideal gas upon inserting wall. As the temperature increases, the entropy change also increases. This is because at higher temperatures, the gas molecules have more energy and are more likely to collide and interact with each other, resulting in a greater increase in disorder and randomness.

5. Can the entropy change of an ideal gas upon inserting wall be negative?

Yes, the entropy change of an ideal gas upon inserting wall can be negative. This occurs when the gas is at a lower temperature and the insertion of the wall causes the gas molecules to become more ordered. In this case, the entropy change will be negative, indicating a decrease in disorder and randomness.

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