- #1
FredT
- 7
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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!
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!
