4 ms·

>That's not how a mercury thermometer works. The mercury "drops" when the temperature of the mercury goes down. This happens when the is a flow of energy betwee

>That's not how a mercury thermometer works. The mercury "drops" when the temperature of the mercury goes down. This happens when the is a flow of energy between the thermometer and the matter inside the box. If all the particles were concentrated elsewhere there would be no interaction, no transfer of energy, no change in the mercury level. (Again, I'm considering thermal contact which is the main effect in play and and ignoring radiation energy losses.) More pedantism. I'm using an example to make a point and I CLEARLY already edited the example enough times so that it's obvious that I'm Not building a physically accurate model. Yes as you said it is completely irrelevant. >But if only the particles in the vicinity of the thermometer matter for the local temperature number that you take as describing the macrostate you would get the same reading (and the same entropy) if the rest of the particles changed positions as long as they remained out of the vicinity of the thermometer. Is that wrong? No that's right. The particles are large in number. Any state where no particles are in the viscinity of the thermometer is a low probability. All microstates that encompass this property occupy at the 0 temperature macrostate. >The main point is that instead of having the balls "positioned near one corner in the cube" they could be positioned in exactly the same relative configuration (the same concentration) near any other corner and the thermometer reading would be different. The entropy is not directly related to the concentration - it depends also on the location of the particles relative to the thermometer. Or maybe the thermometer reading would be same when the particles are in any corners but then it will also be the same for other relative positions so you would also have different levels of concentration corresponding to the same entropy. In this definition macrostate is related to vicinity. And in a physical thermometer in reality it is also directly related to particles in actual contact with the thermometer. Vicinity matters for both cases. >I was trying to point out that having a concentration of the particles (different from the homogeneous equilibrium state) doesn't automatically mean lower entropy in your example. The same relative position of the particles among themselves can correspond to different temperatures in your thermometer - including the equilibrium temperature. (The idea was that if the concentrated particles are too fa" the temperature is "too cold". And maybe if they are too close the temperature is "too hot". But there is some goldilocks intermediate distance such that if you put there the initial concentrated state the temperature according to you would be "just right".) You're not getting it. The entropy states I'm describing are so low in probability that they basically never will happen in your lifetime or the lifetime of this universe. The reality is, if particles are concentrated in the corner of a box then yes, a thermometer will register 0, but you will never see this. They don't jive with your intuition of temperature because of this. But also because the word temperature is poorly defined when applied to a box. What does it mean when you say "The temperature of the room." What part of the room at what point in time? That's why I referenced the thermometer, to prevent this type of tangent in the discussion. There's also ambiguities like what is the temperature of a volume of space smaller than any particle can occupy? But it's pointless to discuss all of this because this isn't a discussion about anything other then linguistics. We are arguing about language and vocabulary here and that to me is not an interesting thing to talk about. It's an illusion. It's like when people argue about "what is life?" without realizing they're just arguing about the definition of a arbitrary vocabulary word. It's sort of what's going on here, I believe. If you are in agreement with me that entropy is independent of knowledge then we're good; because as far as I was concerned this was the point you were trying to make.

kgwgk 4y ago
> Any state where no particles are in the viscinity of the thermometer is a low probability. All microstates that encompass this property occupy at the 0 temperature macrostate. Ok. I'm glad to read that we finally agree that in your example -using the macrostate you defined- the entropy of the "particles near a corner" state is not different from the entropy of any other "particles not near the thermometer" state. Right after you said "Temperature as measured by a thermometer is the macrostate. Every possible configuration of particles (microstates) that causes mercury to rise to a certain degree represents a different macrostate." - I asked "How does your configuration where the balls where near one corner in the cube causes mercury to rise to a different level than the configuration where they occupy a larger volume near the center?" You could have answered "it doesn't - that's the same macrostate with the same temperature and the same entropy" back then. Later I pointed out that "Reducing the space occupied by the initial configuration [doesn't change] the temperature - which you say is 0 in all those cases - or the macrostate - which you call absolute zero macrostate in all those cases. The entropy would be the same whenever the particules are more concentrated than in your example - even though they would have lower probability of ocurrence. Don't you agree?" Instead of answering "I don't agree. Entropy is lower when the current macrostate has a low probability of occuring." you could have said "I agree. I describe the temperature as zero in all those cases, it's the same macrostate and the entropy will be the same." Better late than never, anyway. > the word temperature is poorly defined when applied to a box. I agree! You're the one who picked the reading of that thermometer as the thing that would determine the macrostate and the entropy - and maintained that higher concentrations would mean different thermometer readings and lower entropy. > If you are in agreement with me that entropy is independent of knowledge then we're good; because as far as I was concerned this was the point you were trying to make. If we agree that the entropy is not a physical property of (the microstate of) the system but a property of a particular (thermodynamical) description of the system - and that different descriptions of the same physical system are possible resulting in different entropies - we're good. That's the clarification I wanted to make.
- deltasevennine 4y ago
  >Ok. I'm glad to read that we finally agree that in your example -using the macrostate you defined- the entropy of the "particles near a corner" state is not different from the entropy of any other "particles not near the thermometer" state. This has been the definition since I brought it up. That's how thermometers work. It's the obvious consequence of my description and it's how physicall thermometers generally work. You never made it clear that was your problem with it. Well, now that we're both clear there is no problem with it, I think initially it most likely it just didn't jive with your intuition about temperature. >You could have answered "it doesn't - that's the same macrostate with the same temperature and the same entropy" back then. I did answer this: "The balls have to touch thermometer. Otherwise the thermometer observes nothing." You failed to pick up on what I meant. If the balls don't touch the thermometer is means "it doesn't" change the thermometer and therefore it doesn't change the macrostate. You just didn't get it. OK you can accuse me of not explaining it thoroughly. But I can equally at the same time accuse you of not being capable to interpret what I said. I think what's going on here is that you're too stuck in your headspace of thinking that your intuition of entropy was more accurate then mine and you wanted me to come to this realization. I think what happened here is the reverse of this. Your intuition about entropy was less crystallized then mine and most of the communication issues we had was because you thought it was the other way around. >Instead of answering "I don't agree. Entropy is lower when the current macrostate has a low probability of occuring." you could have said "I agree. I describe the temperature as zero in all those cases, it's the same macrostate and the entropy will be the same." I told you to refer to my explanation of the macrostate. Yeah in all those cases it will be the same. Ok fine. I could've said that. But I didn't realize that was what you were hung up on. To throw it back at you, you could've said this: "it doesn't make sense to me that different concentrations of particles in different parts of the box yield the same temperature reading AKA the macrostate. Please explain how this can be possible" But again I think you didn't realize this was your hang up. I think you thought the my definition of macrostate was a "bad" or something and you were trying to make me realize it? >I agree! You're the one who picked the reading of that thermometer as the thing that would determine the macrostate and the entropy - and maintained that higher concentrations would mean different thermometer readings and lower entropy. Yeah I picked it because it's the most intuitive one to illustrate rising entropy. The "2nd law". It's the classic model everyone has in there heads of the "heat death" of the universe. There are technical issues with the word, but it's the most commonly used one, and we only discussed those technicalities because of a fundamental misunderstanding on your end. IF the intuition was correct, the technicalities do not need to be discussed, or thought about. >If we agree that the entropy is not a physical property of (the microstate of) the system but a property of a particular (thermodynamical) description of the system - Sort of. Entropy is directly tied to macrostate, but macrostate is determined by microstates. There is a relationship here from entropy to microstate but not direct. Also ALL possible macrostate configurations, ARE independent of knowledge of the system. There is no case where knowledge can influence it. There is no case where your initial reply: "If you know the positions and velocities of the balls at all times arguably the entropy is always zero." is correct. Unless of course you define a macrostate where it's zero all the time. But obviously what you're saying here is that knowledge changes the entropy. Which is not true.

kgwgk 4y ago

> Any state where no particles are in the viscinity of the thermometer is a low probability. All microstates that encompass this property occupy at the 0 temperature macrostate. Ok. I'm glad to read that we finally agree that in your example -using the macrostate you defined- the entropy of the "particles near a corner" state is not different from the entropy of any other "particles not near the thermometer" state. Right after you said "Temperature as measured by a thermometer is the macrostate. Every possible configuration of particles (microstates) that causes mercury to rise to a certain degree represents a different macrostate." - I asked "How does your configuration where the balls where near one corner in the cube causes mercury to rise to a different level than the configuration where they occupy a larger volume near the center?" You could have answered "it doesn't - that's the same macrostate with the same temperature and the same entropy" back then. Later I pointed out that "Reducing the space occupied by the initial configuration [doesn't change] the temperature - which you say is 0 in all those cases - or the macrostate - which you call absolute zero macrostate in all those cases. The entropy would be the same whenever the particules are more concentrated than in your example - even though they would have lower probability of ocurrence. Don't you agree?" Instead of answering "I don't agree. Entropy is lower when the current macrostate has a low probability of occuring." you could have said "I agree. I describe the temperature as zero in all those cases, it's the same macrostate and the entropy will be the same." Better late than never, anyway. > the word temperature is poorly defined when applied to a box. I agree! You're the one who picked the reading of that thermometer as the thing that would determine the macrostate and the entropy - and maintained that higher concentrations would mean different thermometer readings and lower entropy. > If you are in agreement with me that entropy is independent of knowledge then we're good; because as far as I was concerned this was the point you were trying to make. If we agree that the entropy is not a physical property of (the microstate of) the system but a property of a particular (thermodynamical) description of the system - and that different descriptions of the same physical system are possible resulting in different entropies - we're good. That's the clarification I wanted to make.

deltasevennine 4y ago
>Ok. I'm glad to read that we finally agree that in your example -using the macrostate you defined- the entropy of the "particles near a corner" state is not different from the entropy of any other "particles not near the thermometer" state. This has been the definition since I brought it up. That's how thermometers work. It's the obvious consequence of my description and it's how physicall thermometers generally work. You never made it clear that was your problem with it. Well, now that we're both clear there is no problem with it, I think initially it most likely it just didn't jive with your intuition about temperature. >You could have answered "it doesn't - that's the same macrostate with the same temperature and the same entropy" back then. I did answer this: "The balls have to touch thermometer. Otherwise the thermometer observes nothing." You failed to pick up on what I meant. If the balls don't touch the thermometer is means "it doesn't" change the thermometer and therefore it doesn't change the macrostate. You just didn't get it. OK you can accuse me of not explaining it thoroughly. But I can equally at the same time accuse you of not being capable to interpret what I said. I think what's going on here is that you're too stuck in your headspace of thinking that your intuition of entropy was more accurate then mine and you wanted me to come to this realization. I think what happened here is the reverse of this. Your intuition about entropy was less crystallized then mine and most of the communication issues we had was because you thought it was the other way around. >Instead of answering "I don't agree. Entropy is lower when the current macrostate has a low probability of occuring." you could have said "I agree. I describe the temperature as zero in all those cases, it's the same macrostate and the entropy will be the same." I told you to refer to my explanation of the macrostate. Yeah in all those cases it will be the same. Ok fine. I could've said that. But I didn't realize that was what you were hung up on. To throw it back at you, you could've said this: "it doesn't make sense to me that different concentrations of particles in different parts of the box yield the same temperature reading AKA the macrostate. Please explain how this can be possible" But again I think you didn't realize this was your hang up. I think you thought the my definition of macrostate was a "bad" or something and you were trying to make me realize it? >I agree! You're the one who picked the reading of that thermometer as the thing that would determine the macrostate and the entropy - and maintained that higher concentrations would mean different thermometer readings and lower entropy. Yeah I picked it because it's the most intuitive one to illustrate rising entropy. The "2nd law". It's the classic model everyone has in there heads of the "heat death" of the universe. There are technical issues with the word, but it's the most commonly used one, and we only discussed those technicalities because of a fundamental misunderstanding on your end. IF the intuition was correct, the technicalities do not need to be discussed, or thought about. >If we agree that the entropy is not a physical property of (the microstate of) the system but a property of a particular (thermodynamical) description of the system - Sort of. Entropy is directly tied to macrostate, but macrostate is determined by microstates. There is a relationship here from entropy to microstate but not direct. Also ALL possible macrostate configurations, ARE independent of knowledge of the system. There is no case where knowledge can influence it. There is no case where your initial reply: "If you know the positions and velocities of the balls at all times arguably the entropy is always zero." is correct. Unless of course you define a macrostate where it's zero all the time. But obviously what you're saying here is that knowledge changes the entropy. Which is not true.