Implications of infinity on positional entropy?

In summary, the conversation discusses the concept of entropy and its explanation in terms of the number of possible positions molecules can take in space. It is believed that gases have higher entropy than liquids and solids due to the larger number of positions available. However, the speaker questions this explanation, suggesting that in an infinitesimal universe, both parties would have an equal number of possible moves. They ask for clarification on the concept of positional entropy and whether the textbook's explanation is flawed.
  • #1
FredT
7
0
I just read the chapter on entropy in my chemistry text. The book described entropy in terms of possible positions in space that a molecule could take (or even ways in which the atoms within a molecule can shift and rotate). The claim was that gasses had higher entropy than liquids and liquids higher than solids because there are more positions available to the molecules in the former rather than the latter. Gasses at lower pressures have greater entropy than gasses at higher pressures because the same number of moles in a larger container has access to a greater number of possible locations.

I have a bit of an issue with this explanation. I believe it's generally accepted that the "grid" of space is infinitesimal - that I can always move half the distance to an object, right? Let's play a game in our infinitesimal universe. We each have a coin and a two dimensional surface on which we place our coin. Your surface is 20 cm x 20 cm and my surface is only 10 cm x 10 cm. We take turns moving our coins. The only rule is that you cannot return your coin to a position it has assumed previously.

According to what I read in my textbook, you would always win the game because your surface is larger than mine, so there are more places where you could put your coin. But I think it's pretty clear that neither of us would win. I can guarantee you that if the coordinate system of our universe truly is infinitesimal in nature I will ALWAYS find a spot for my next move! Despite you having a larger playing area, we both have the same number of possible moves: infinitely many!

The concept of infinity can be strange and rather confusing. Could someone please enlighten me as to why the concept of positional entropy is correct? Please let me know if the description of my confusion was not clear enough.

Thanks!
 
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  • #2
Look at the spread of the molecules in a given volume instead of the number of positions a given molecule can have.
 
  • #3
So are you saying that the explanation in my textbook is flawed? Or that I'm reading the explanation the wrong way?
 

1. What is positional entropy?

Positional entropy is a concept in statistical mechanics that measures the amount of uncertainty or disorder in the positional coordinates of a system. It is a measure of the number of possible positions or arrangements that a system can take on, and therefore describes the randomness or disorder in the system.

2. How does infinity affect positional entropy?

Infinity has a significant impact on positional entropy because it represents the upper limit of the number of possible positions or arrangements that a system can have. As the number of possible positions increases towards infinity, the positional entropy also increases, indicating a higher level of disorder and uncertainty in the system.

3. What are the implications of infinity on positional entropy?

The implications of infinity on positional entropy are vast. As the number of possible positions or arrangements increases towards infinity, the system becomes more unpredictable and chaotic. This can have consequences in various fields, such as physics, chemistry, and computer science, where understanding and predicting the behavior of complex systems is crucial.

4. Can positional entropy ever reach infinity?

No, positional entropy cannot reach infinity as it is only a mathematical concept used to describe the amount of disorder or uncertainty in a system. In reality, there are always limitations to the number of possible positions or arrangements that a system can have, even if it is a very large number.

5. How is positional entropy related to thermodynamics?

Positional entropy is closely related to thermodynamics, specifically the second law of thermodynamics, which states that the entropy of a closed system will always increase over time. This law applies to both thermal entropy (related to heat energy) and positional entropy. As a system approaches infinity, its positional entropy will also increase, leading to a state of maximum disorder or entropy.

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