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> I understand that's what they mean, but this is the part that I think is either trivial or wrong. That is, depending on your choice you'll of course get diffe
by kgwgk 2y ago
> I understand that's what they mean, but this is the part that I think is either trivial or wrong. That is, depending on your choice you'll of course get different values, but it won't change anything about the system. It's basically like choosing to measure speed in meters per second or in furlongs per fortnight, or choosing the coordinate system and reference frame: you get radically different values, but relative results are always the same.
I would agree that it's trivial but then it's equally trivial that it's not just like a change of coordinates.
Say that you choose to represent the macrostate of a volume of gas using either (a) its pressure or (b) the partial pressures of the helium and argon that make it up. If you put together two volumes of the same mixture the entropy won't change. The entropy after they mix is just the sum of the entropies before mixing.
However when you put together one volume of helium and a one volume of argon the entropy calculated under choice (a) doesn't change but the entropy calculated under choice (b) does increase. We're not calculating the same thing in different units: we're calculating different things. There is no change of units that makes a quantity change and also remain constant!
The (a)-entropy and the (b)-entropy are different things. Of course it's the same concept applied to two different situations but that doesn't mean it's the same thing. (Otherwise one could also say that the momentum of a particule doesn't depend on its mass or velocity because it's always the same concept applied in different situations.)
- tsimionescu 2y ago> However when you put together one volume of helium and a one volume of argon the entropy calculated under choice (a) doesn't change but the entropy calculated under choice (b) does increase. We're not calculating the same thing in different units: we're calculating different things. There is no change of units that makes a quantity change and also remain constant! Agreed, this is not like a coordinate transform at all. But the difference from a coordinate transform is that they are not both equally valid choices for describing the physical phenomenon. Choice (a) is simply wrong: it will not accurately predict how certain experiments with the combined gas will behave.
- kgwgk 2y agoIt will predict how other certain experiments with the combined gas will behave. That's what people mean when they say that the entropy is not an "objective" property of a physical system: that it depends on how we choose to describe that physical system - and what experiments we can perform acting on that description.
- tsimionescu 2y agoWhat would be an example of such an experiment? By my understanding, even if we have no idea what gas we have, if we put it into a calorimeter and measure the amount of heat we need to transfer to it to change its temperature to some value, we will get a value that will be different for a gas made up of only argon versus one that contains both neon and argon. Doesn't this show that there is some objective definition of the entropy of the gas that doesn't care about an observer's knowledge of it?
- kgwgk 2y agoActually the molar heat capacity for neon, or argon, or a mixture thereof, is the same. These are monotomic ideal gases as far as your calorimeter measurements can see. If the number of particles is the same you’ll need the same heat to increase the temperature by some amount and the entropy increase will be the same. Of course you could do other things to find out what it is, like weighing the container or reading the label.
- tsimionescu 2y agoNo, they are not. The entropy of an ideal monatomic gas depends on the mass of its atoms (see the Sackur–Tetrode equation). And a gas mix is not an ideal monatomic gas; its entropy increases at the same temperature and volume compared to an equal volume divided between the two gases. Also, entropy is not the same thing as heat capacity. It's true that I didn't describe the entropy measurement process very well, so I may have been ambiguous, but they are not the same quantity.