The h Bar - 2016-09-09 (page 1 of 4)

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user218912

12:51 AM

hello

1:03 AM

29 unreal images from a man who's spent 29 years inside a legendary physics lab / businessinsider

1 hour later…

user228700

2:21 AM

@JohnRennie Hello sir :) I was wondering if it would be OK with you to discuss entropy for a little bit.

@KaumudiHarikumar He's asleep.

1 hour later…

user228700

3:26 AM

Yeah, I realized that a bit later :P I'll wait.

user116211

3:39 AM

@KaumudiHarikumar Leave the message pinging him; he would respond if he wants after he comes.

user228700

I'm sorry, but how to ping him?

@JohnRennie

user228700

Okay, thanks :)

user228700

Also, if any of you wouldn't mind discussing it with me, then that would do as well...

user228700

4:02 AM

I realize that most of you are specializing in much more advanced fields of physics and it really is true that none of you would gain very much from discussing a bit about entropy with a person who has just graduated high school. Still, it would help me out quite a lot, especially since I don't have any teachers with whom I can discuss this. I'd post a question but I am certain that it would invetiably lead to a discussion here at some point.

user228700

So, if anybody wants to discuss this, please let me know here. I'm sorry for the spam. Thanks :)

user116211

Just leave your query; anyone interested would help you.

user228700

Here? I'll type it here?

user228700

4:15 AM

Guess I'll wait.

@KaumudiHarikumar: morning

user228700

@JohnRennie Morning sir :)

You don't need to call me "sir" - just "John" will do :-)

user116211

Is Zorn's Lemma equivalent to Axiom of Choice?

user228700

Oh, but you're so much more knowledgrable and I'm assuming that you're also older. Can't help it :P But alright :) Do u mind talking to me a bit about entropy?

user116211

4:18 AM

I'll have to dig more.

user116211

@KaumudiHarikumar He is the classic old nerd of our community.

I'm willing to give it a go, though thermodynamics isn't one of my strongest fields. What did you want to know?

user228700

No problem! I'm not going to ask about complicated stuff so I'm sure that you will be able to help me out.

@MAFIA36790 classic old nerd - yup, that's me :-)

user116211

;D

user228700

4:21 AM

So I'm currently reading "Resnick and Halliday" to learn about entropy and it's turning out to be very difficult because of all these different statements of the second law of thermo.

user228700

@MAFIA36790 I figured :D

user116211

Ah! Here it goes:

user116211

1

Q: Axiom of Choice and Zorn's Lemma Equivalence: some intuition

$$ \text{Axiom of Choice $\Rightarrow$ Zorn's Lemma } $$ $$\text{Axiom of Choice $\Leftarrow$ Zorn's Lemma } $$ I feel mathmatically immature to go through these proofs now. My quesiton therefore is: Is there an intuitive way/example/ausiliary proof/exercise to grasp their being-the-sameness? ...

set-theory intuition axiom-of-choice

@KaumudiHarikumar Is that their "Fundamentals of Physics" book?

user116211

@KaumudiHarikumar A side-comment; there are much better treatises than Resnick and Halliday in thermodynamics; I never find that book good enough in the topic. They touched most of the topics but lacked rigor.

user228700

4:24 AM

It's called "Principles of Physics". 9th edition.

user116211

@JohnRennie I never understood why they published two books in different names but both having more-or-less the same contents.

user228700

@MAFIA36790 The thing is that for the exam I'm preparing, I don't need to know everything that's given in the book, even! The problem with me is that I absolutely need to know what I'm doing and for every topic other than entropy, the explanations are satisfactory for students at my level

user116211

in Chemobot, 12 mins ago, by xkcd

Hang on, I just remembered another thing I'm right about. See...

Hi everybody

user116211

@DanielSank o/

4:29 AM

@KaumudiHarikumar part of the problem is that there are different ways of approaching the idea of entropy.

@MAFIA36790 \o

user228700

In the book, they've stated that there are two ways...the microscopic way(statistical) and the macroscopic way...

user228700

That's correct, right?

@KaumudiHarikumar yes, thats a common way of approaching it.

user228700

Okay. I haven't gotten to the statistical way yet...

user116211

4:32 AM

@KaumudiHarikumar They only discussed about the equilibrium case; the Boltzmann entropy.

user228700

I've become stuck at the macroscopic way. The problem is that at this point, I've watched about two lectures and read some articles on the internet but I've encountered more and more ways to put the same idea into words and I'm spectacularly confused at this point.

user228700

*Two looong lectures.

user228700

@MAFIA36790 Oh, I see.

@KaumudiHarikumar thermodynamics lectures all feel long :-)

user228700

@JohnRennie Okay :P But yes, that is the problem. To give you an idea, I'll type some of the different ways that I've come across...

user228700

4:37 AM

The most basic videos describe entropy as "a measure of disorder" and I learned to stop watching those videos awhile ago.

@KaumudiHarikumar that's really the stat mech approach

user228700

Yep, I realize.

user228700

This is what my copy of the book says: "If an irreversible process occurs in a closed system, the entropy S of the system always increases; it never decreases.

There is an ambiguity about what the phrase closed system means, but basically that's a fair enough statement.

user228700

The first doubt that comes to mind is "Exactly what do they mean by a closed system", because I don't think they mean that system in which matter can't be exchanged with the surroundings but energy can.

user228700

4:41 AM

Yes, exactly.

Yes, I agree. Because $dS=dQ/T$ a closed system can lower its entropy by transferring heat to its surroundings.

So I think they mean isolated system

My laptop's power cable fucking failed.

Out of the blue

user228700

@JohnRennie Okay, this makes sense. The universe is an isolated system, yes?

@KaumudiHarikumar as far as we know yes it is, though there are pitfalls in talking about the universe because it may be infinite.

$80 for a new one.

4:44 AM

Dealing with infinite systems can be tricky.

@yuggib Guess I'm not getting Evans.

user228700

@JohnRennie Yes, okay.

user228700

But for the time being, let us consider that the universe is an isolated system because my book says so :P (I know that it can be frustrating to have to deal with the oversimplified versions of theories and other concepts, but I hope that you will please bear with me.)

It's common to take the universe as an isolated system, so that's a fair enough starting point.

@JohnRennie computer guru pls

user228700

4:50 AM

Okay. So, my second doubt is this; how is it possible for us to talk about the entropy of the system alone?

@0celo7 my expertise is at your command.

if my computer doesn't work with my charger but it does work with my roommate's, the charger itself is kaput, right?

@0celo7 yes

it's not the computer that has an issue

why would a charger just decide to break

@0celo7 yes, but don't invoice me if you buy a new charger and it doesn't work.

user228700

4:51 AM

@0celo7 I'm sorry about your charger :(

@JohnRennie Is there anything I should try?

@0celo7 power supplies fail more often than motherboards, so my guess would be you just need a new PSU. You can get one cheap on ebay if you don't mind waiting. Otherwise yes they are a it pricy.

@0celo7 if your laptop charges from your friends PSU then it's your PSU that's dead.

I need one tomorrow.

I need one by 3:30 tomorrow, actually.

@0celo7 Amazon next day delivery it is then

@JohnRennie I doubt we get that here

And there's an Apple vendor on campus.

I'll go after Analysis.

4:54 AM

@KaumudiHarikumar I'm not sure I see why there is a problem. You could in principle choose any chunk of the universe and that chunk will have some reasonably well defined entropy.

@JohnRennie yeah but is there anything I can do about it?

give it a good jiggle?

I dunno

user228700

@JohnRennie What I mean is, there are many processes for which if we talk only about the system, it seems like the entropy is actually decreasing, no?

@0celo7 PSUs do blow. Short of opening it up and getting out your soldering iron there's nothing you can do about it.

@JohnRennie There's a soldering iron in my lab.

@KaumudiHarikumar for a closed system or an isolated system?

4:56 AM

Sigh.

I need to sleep.

Thanks.

Cheerio.

@0celo7 yes, but you'd need the replacement parts, testing equipment and the circuit diagram. It's a non-starter.

user228700

@JohnRennie Erm, I'm not sure. I don't understand it...

@JohnRennie I was going to get a PDE book on sale, but now I'm buying a charger. I'm very salty.

@KaumudiHarikumar Well give me an example of a process that you think lowers the entropy of your system.

And this is after my cousin stole my iPad charger!

user228700

4:58 AM

So I was watching that lecture and the prof. talked about the crystallization of hypo.

hypo = sodium thiosulphate?

user228700

Sodium thiosulphate :)

user228700

Yes.

Ok, carry on ...

user228700

According the "disorder" model(Please forgive me for being so sketchy), the entropy of the system defined as the petri dish containing the hypo solution is supposed to decrease on crystallization, no?

5:03 AM

@MAFIA36790 Do you high-five everyone, or is this a special thing I get?

Just for clarity, are we talking about the hypo dissolving in its own water of crystallisation as it is heated, then forming crystals again as it cools?

Hi @KaumudiHarikumar, welcome to the site.

user228700

@JohnRennie Yep, I think so.

I like the part on your profile about reducing world suck.

user228700

@DanielSank Hi :) Thanks!

5:04 AM

@KaumudiHarikumar OK, so as it cools dQ is negative, i.e. heat leaves the system, so $dS=dQ/T$ is negative.

user228700

Okay, now I'm confused about something else. When we're talking about an exothermic reaction, heat leaves the system...yeah?

@KaumudiHarikumar Yes.

user228700

Okay, so in this case, crystallization of hypo releases heat. The process is exothermic.

Yes

user228700

So...heat leaves the system and so the entropy decreases...yeah?

5:08 AM

Yes

user228700

Yeah, so clearly, this seems like a violation of the second law but only if we're focused on the system alone.

user228700

If we take the surroundings into account, it becomes clear that the net entropy increase.s

Correct, the entropy of the surroundings increases because heat is transferred into it (from the hypo)

user228700

Okay, but the statement only talks about the system...

user228700

At least the one given in my book.

5:11 AM

I think this is another example of the confusion between a closed system and an isolated system

user228700

How so..?

user116211

@DanielSank Well, I do it to many; yuggib to be mentioned among them; it's a common practice, isn't it?

The second law states the total entropy of an isolated system always increases over time, or remains constant in ideal cases - from Wikipedia

user228700

Okay, so if the statement actually meant isolated system in place of closed system, we would've taken the surroundings into account too? 'Cause it's NOT an adiabatic process...

Yes, the petri dish of hypo is obviously not an isolated system because it exchanges heat with its surroundings.

So the second law doesn't apply to just the dish of hypo.

user228700

5:14 AM

Yeah, okay. So, if heat exchange is taking place, we take all those parts of the system into account too, yes?

Yes

user228700

Okay. So basically, the law says that change in entropy can either increase or be zero but never negative, yes?

The change in entropy of an isolated system can either increase or be zero but never negative.

user228700

Yeah, that's what I meant, sorry.

user228700

So okay. Can I ask you one more?

user228700

5:18 AM

*some more :P

Yes, go ahead.

It's early in the morning here, and I'm just drinking coffee and putting off doing any real work. So now is a good time to talk about physics :-)

user228700

Supposedly, entropy doesn't really have a physical significance...correct?

Hmm, I'm not sure what that statement means.

user228700

@JohnRennie I see :) It's almost noon here and this is real work for me :P

Entropy isn't something you can measure - like mass or volume.

user228700

5:20 AM

Okay...

But obviously it has great physical importance.

user228700

Yes, of course, in that it gives us the direction of time and all, yeah?

user116211

@KaumudiHarikumar Well, among the thermodynamics perspective, there are many approaches too; the axiomatic approach of Caratheodory to be mentioned among them.

@KaumudiHarikumar The direction of time is a diversion.

user228700

Okay..? Please go on...

5:21 AM

Most thermodynamic quantities can't be measured - Gibbs free energy for example.

user228700

Yeah, that too. Oh God, nothing has ever confused me mor.e

So entropy is not unusual in this respect

user228700

Okay...

user228700

So this quantity was defined...why?

user116211

This is bothering when the users use classical-mechanics to ask petty kinematics questions ;(

5:23 AM

In thermodynamics, as opposed to stat mech, a lot of the concepts used are a bit unintuitive. You just need to get used to it.

Entropy is used because it turns out to be extremely useful in predicting how systems behave.

user228700

Okay...

That doesn't mean it's a thing like mass is a thing.

user116211

It's a thermodynamic potential.

In thermo it's more like an abstract idea though a very useful one.

@MAFIA36790 I would have said that was more the Gibbs free energy i.e. the chemical potential

user228700

So, wait, I need to get used to the fact that loads of quantities in physics are defined not because they exist or anything...but because they're useful to describe the universe?

user228700

5:25 AM

Like imaginary numbers in math?

Welcome to thermodynamics :-)

To be fair most of physics is more concrete than this.

I think the problem arises because thermodynamics isn't fundamental. It arises as the continuum limit of stat mech.

user116211

In thermodynamics, it is not the definition that matters, but rather it is the difference or change that matters.

user228700

Phew, okay :P

user116211

@JohnRennie That's the core point.

And in stat mech we deal with concrete properties like the energy and momentum of individual particles.

user228700

5:27 AM

@JohnRennie I have no idea what you just said.

@KaumudiHarikumar Suppose you look at your disk of hypo at really small scale so you can see individual molecules.

user116211

@KaumudiHarikumar This is about thermodynamic limit.

user228700

@JohnRennie Alright...

This actually makes things simple because molecules are particles with an energy and a momentum.

They collide with each other and exchange energy and momentum, but it's all pretty straightforward.

user228700

@JohnRennie But there are a LOT of these particles...

5:29 AM

@KaumudiHarikumar Exactly. So you have to somehow throw away all the detail, e.g. which molecule is going in what direction, but keep enough info to still describe the properties of the whole system.

And that's what thermodynamics does.

user228700

@JohnRennie Riiight. Okay...

user116211

@KaumudiHarikumar When the system becomes infinitely large, measurable fluctuations from the most likely state ceases to occur; and here is what we call it thermodynamic limit. And now you are in the realms of thermodynamics.

@KaumudiHarikumar But the process of moving from individual molecules to bulk properties introduces concepts like entropy and Gibbs free energy that are hard to relate to anything specific.

@MAFIA36790 I have no idea. I learned it from you.

Hey, anyone around here know any online resources where I might be able to easily look up Russian declensions of words?

user228700

@JohnRennie Okay...

5:31 AM

@KaumudiHarikumar We end up with a few apparently simple ideas, but when you look into what exactly those ideas mean it all gets horrifically confusing.

Like, I type "гриба" and then it tells me all the declensions...

user228700

@JohnRennie Okay, I'm glad that it's confusing for everybody at least :P So okay, entropy is defined so we can make better sense of all this at the macroscopic level...yeah?

So you just need to accept that entropy is a thing, and it's described by these equations, and when you work through the equations it eventually tells you how your system behaves.

user228700

Right, okay. Then what's all this about disorder..?

@KaumudiHarikumar that's the statistical mechanics approach

5:34 AM

I realize I'm late to the party, but entropy is not a mysterious black magic.

It's pretty easy to understand.

When you look at things that way you are looking at the system in detail and asking how many ways there are of arranging it.

@DanielSank It totally is! :-)

@JohnRennie Glad we agree.

user116211

@DanielSank ohh; but I've not invented it; it's a conventional emoticon.

Entropy is black magic and if you study it your soul will go to hell!

user228700

@JohnRennie Okay...

user228700

5:36 AM

@DanielSank Haha, okay. I'm not frightened by it or anything. I just didn't have the best sources at hand...

Stat mech and thermodynamics approach the description of systems from opposite ends, sort of.

user228700

Didn't :)

user228700

@JohnRennie How so..?

Looking back through the chat transcript, @KaumudiHarikumar your question is what entropy means physically, right?

user228700

@DanielSank I mean, it sort of was but not entirely, no.

user228700

5:38 AM

I was confused about the 2nd law and of course, yes, what entropy actually meant but @JohnRennie told me about the whole "define it to use it even though it's not an actual thing" thing and I think I understand that now...

user228700

It's very difficult to be learning thermodynamics on my own :P I don't have any teachers/friends to help me out irl.

@KaumudiHarikumar that's true in thermodynamics, but in stat mech we have a precise definition of the entropy $S=k ln W$.

Thermo and stat mech and conceptually very different.

user228700

Yeah, that. I read that. Here W is the total number of...what?

@KaumudiHarikumar I strongly recommend you to learn from the book by Reif if you can get it.

W is the number of ways of arranging the system - now you'll ask what I mean by that :-)

5:40 AM

The book by Callen is also good.

Can we do a very simple example to explain what entropy really means?

user228700

@DanielSank Like I said, right now, I don't have the time to read a lot of it. I'm preparing for an exam and have too many topics to cover so I'm trying to learning as much as I can, as fast as I can.

user228700

@DanielSank Sure :)

@KaumudiHarikumar Oh oh that's different.

user228700

@JohnRennie Of course I will :P

Never mind. I was going to suggest going slowly from a very nice example, but if you're cramming for an exam that might not be worth your time. Your call though.

user228700

5:41 AM

@DanielSank I'm not cramming per se :P My exam isn't until next YEAR.

@KaumudiHarikumar ah

user228700

I definitely have time for the example. Please go on...

user228700

@JohnRennie No, see, I do understand what that means...to a certain extent at least.

@JohnRennie I don't want to interrupt the line of discussion so I'll wait on giving my example unless you want to "yield the floor" as it were.

@KaumudiHarikumar To be honest this gets very complicated very quickly. You need to understand what is meant by the phase space of a system. Until you get to university level I'd be inclined to sweep this one under the carpet.

5:42 AM

@JohnRennie No you don't! :)

Forget phase space.

Daniel thinks everything is easy because he's kind of a mad genius. He even looks like a mad genius :-)

@JohnRennie !

How do you know what I look like?

This octopus picture isn't actually a self portrait, you silly Brit.

You do! I cite your blog photo as evidence!

user228700

Exactly!

@JohnRennie Bollocks, I forgot about that.

5:44 AM

:-)

Going to post some stuff there soon-ish.

Did I use "bollocks" right?

user228700

Wait, what blog?

I recently started a blog, but there's nothing there yet.

@DanielSank Yes, that's the way we Brits would use it :-)

Link to blog

user228700

5:45 AM

I'll check it out, thanks :)

@JohnRennie Very good.

@KaumudiHarikumar Again, there's nothing there yet.

user228700

No, okay, see, I watched a lecture about all this statistical mech. stuff.

user228700

This one:

user228700

Mod-01 Lec-12 Maxwell Boltzmann Statistics

@KaumudiHarikumar Suppose I have one X and one O. Suppose I tell you all the X's are to the left of all the O's. How many possible arrangements of the system are there?

Actually, let's change it slightly.

user228700

5:47 AM

Just one.

Suppose I have some bits. Each bit can be 0 or 1.

If I have one bit, how many different strings can I have?

I can have "0" or "1", so there are two possible strings.

user228700

Only one.

"String" means "sequence of 0's and 1's" here.

user228700

Huh? But you said that you have only one bit-EITHER 1 or 0 right?

user228700

Oh, you meant, okay. I thought that which bit you had was given. Yes, then two.

5:48 AM

Yes, but I ask for the number of possible strings.

Right.

Now I have two bits.

How many strings are there?

user228700

The sequence does matter right?

user228700

'cause 01 is not the same as 10, right?

user228700

Of course it isn't. Sheesh. Sorry. You'd have 4

user228700

Wait, hold on. Did @JohnRennie leave?

No, I'm, still here ...

5:50 AM

I bet @JohnRennie is still around.

Yes, there are four.

Now what if I have N bits? How many strings?

user228700

(2N)! ? 'Cause each bit can be either 1 or 0...

I was trying to show probability current explicit form, but I was not sure whether potential commutes with wavefunction in general (in R-representation)

@KaumudiHarikumar You're right that each bit is 0 or 1, but I'm no sure where you got $(2N)!$.

Do you have mathjax on?

since I can't be sure the exact form of potential if it depends on angle.

or even time dependent.

would anyone be kind enough to shed some light on this matter?

user228700

Oh no, wait, got it wrong.

user228700

5:56 AM

2^N?

user228700

No, it isn't on.

user228700

Should I try to figure out how to switch it on?

It's easy and helpful

dl.dropboxusercontent.com/u/78279253/mathjax.html

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