The h Bar - 2017-10-15 (page 2 of 3)

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4:09 PM

why equilibrium = more entropy?

Anonymous

14

Q: Why does maximal entropy imply equilibrium?

From a purely thermodynamical point of view, why does that entropy have to be a maximum at equilibrium? Say there is equilibrium, i.e. no net heat flow, why can the entropy not be sitting at a non-maximal value? From the second law of thermodynamics, it follows that $S$ never gets smaller and o...

thermodynamics entropy equilibrium

why does heat flow from hot to cold given second law?

do I need to use the fact that somehow temperature is derivative of entropy?

I have never understood the various equivalences between the physical and mathematical laws

in thermodynamics

@0celo7 Hmmmmm

Anonymous

@LeakyNun It's a direct result from the second law of thermodynamics. One of the forms of second law is that heat cannot flow from cold region to hot region unless you do external work on it. The equivalence of all these results can be shown using statistical mechanics and the concept of ensembles

@Blue oh ok

Anonymous

4:14 PM

For example in refrigerators heat does indeed flow from cold regions to hot regions

right

Anonymous

Second law of thermodynamics

The second law of thermodynamics states that the total entropy can never decrease over time for an isolated system, meaning - a system which neither energy nor matter can enter or leave. The total entropy can remain constant in ideal cases where the system is in a steady state (equilibrium), or undergoing a reversible process. In all other real cases, the total entropy always increases and the process is irreversible. The increase in entropy accounts for the irreversibility of natural processes, and the asymmetry between future and past. Historically, the second law was an empirical finding that...

Anonymous

This article explains most of the forms of the laws

I would say you're right to link it with the definition of temperature, though.

Anonymous

Yeah, temperature is defined in terms of entropy

4:16 PM

@BalarkaSen And using the Poincaré conjecture in the 3-fold case is really a nuclear strike

suppose I have two systems in contact at temperatures $T_1<T_2$.

@0celo7 Since $M$ is a hypersurface in $S^5$, the complement breaks into two components $X$ and $Y$. But call $X$ and $Y$ to be a thickening of these two.

$X \cap Y$ is a line bundle neighborhood of $M$, which def rets to $M$, which is s.c.

So in fact you get to apply SvKT to $S^5 = X \cup Y$ and get $\pi_1(S^5) = \pi_1(X)*\pi_1(Y)$

Which is 0, hence the two components of the free product are zero

There's nothing special about embedded spheres

Anonymous

2

A: Equivalence of the statements of the second law of thermodynamics

One way in which to show the two statements are equivalent is to show that if one of them is violated then so is the other. We show here that if the Kelvin statement is violated, then so is the Clausius statement. Imagine there were such a things as a perfect heat engine: For each joule of heat ...

Anonymous

This answer gives a brief idea ^

Then that means $\frac{\partial S_1}{\partial U_1}<\frac{\partial S_2}{\partial U_2}$ where $U_1,U_2$ are the respective internal energies.

Anonymous

4:19 PM

4

A: 2$^\text{nd}$ law of thermodynamics: equivalence of statements

Not sure if this is the 'proof' you're looking for, but here goes: Imagine we have a system $S$ that undergoes a cyclic process (which can be reversible or irreversible). During the process, S takes in amounts of heat $Q_1, Q_2, \dots, Q_n$ (which may of course be negative) from thermal reservoi...

hrm. brain not working right now.

Anonymous

@Semiclassical Before that you'd need to explain how you landed up with dS/dU (as the definition of T):P

Constantine Black

Could I maybe think of the isospin here as something analog to color for QCD and try and figure from Srednicki' s chapter on Feynman rules for QCD what to do?

If I suppose that the two systems remain at constant volume and particle number, then I can take those derivatives as total rather than partial

Anonymous

@Semiclassical Yep

Anonymous

4:21 PM

$S(U,V,N)$

so that's $\frac{dS_1}{dU_1}<\frac{dS_2}{dU_2}$

I've accidentally started a discussion about the linkage of entropy and temperature :D

Anonymous

@LeakyNun It's actually complicated =P You have to move back and forth several times to relate those two

what I want to say now is that, if both systems are to increase in entropy, then system 1 must gain energy from system 2

i.e. $dU_1 = -dU_2$.

not sure how to say that in a legit way, though

Well, if both systems are isolated from their environment, then $U_1+U_2$ is constant.

so I guess that legitimates it

oh doh

1/T = dS/dU

well that's embaressing

meh. i'm not awake enough to be doing thermodynamics right now :P

@BalarkaSen The point being that the normal bundle is always going to be trivial and so SvK applies easily?

4:30 PM

There is an empty box which consists of a single neutron. Calculate the pressure on the walls of the container.

How do I solve it without probabality based arguments?

There is just one neutron :/

Calculate the ground state energy as a function of the box size (it's just a particle in a box)

Oo

@0celo7 Well, the normal bundle deformation retracts to M, is the point. And M is simply connected, hence so is the normal bundle.

@JohnRennie ground state energy?

SvK applies even when the intersection is not simply connected, it's just that it's much simpler (the amalgamated product becomes free product)

4:32 PM

sure. quantum mechanics 101.

Then the change in the ground state energy with box size gives you the pressure because the change in energy is equal to $PdV$

I tried to use KTG and use that the speed distribution in all directions is uniform

KTG?

KTG?

jinx

4:33 PM

Kinetic theory of gas

I doubt the question means you to use kinetic theory

I would guess it's a quantum mechanics question

eh, that's describing a gas of many particles. it might be interesting to see what that predicts, but i doubt very much what's intended.

Anonymous

Kinetic theory doesn't work for one neutron

@Yashas see:

Particle in a box

In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example, a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum...

Assuming the neutron is in the ground state the energy is the energy of the ground state.

And that energy decreases as you make the box bigger

Anonymous

Just use $P=-d(E_k)/dV$

4:36 PM

in this case they presumably want a 3D box.

that doesn't make it much different, but it does need to be kept in mind.

Anonymous

$E_k$ is the kinetic energy of the bounded particle (in 3D box)

Anonymous

$E_k=\frac{3h^2}{8ma^2}$

tsk, you gave the game away :P

Anonymous

Heh :P

@Blue don't just give the answer!

Anonymous

4:38 PM

It's just thermodynamics :)

Anonymous

@JohnRennie Oh well :P

just because it's elementary for us...

@BalarkaSen and you get that defo retro because it's trivial, no?

@0celo7 defo retro

I can't picture a twisted normal bundle so maybe I'm wrong

4:38 PM

that's a fun phrase

@Semiclassical autocorrect. It's supposed to be defo retr

ah

@0celo7 No, any vector bundle deformation retracts to it's zero section

Just linear deformation retract fiberwise

@Yashas Since that's just one neutron, for realizable box sizes the pressure would be ridiculously small and you can safely assume $P\approx 0$

Anonymous

@lılostafa Lel

4:40 PM

that may be true, but

don't do that for a problem :P

Anonymous

@lılostafa The engineer in you is showing

though a good question would be "what units would you use for that"

pressure has units of energy density, so eV/nm^3

Anonymous

Is there any special unit for quantum mechanical pressure?

This question appeared in a qualification test for a robotics contest

...huh.

Anonymous

4:42 PM

I don't think so

Anonymous

@Yashas Wut

No idea what a neutron in a box has got to do with robotics

i'm inclined to agree.

Anonymous

That's a science club in disguise

And my QM course is 2 years away

Anonymous

4:42 PM

Opposite to ours

Anonymous

Our science club is a robotics club in disguise

Lol

sign that I'm a physicist:

Anonymous

Oh. BTW how is it going on in IIITH ?

Fine

4:43 PM

understanding the pressure due to a neutron in the ground state: easy

@Semiclassical what is up with Sakurai's dimensions

Anonymous

You seem to be too busy nowadays :)

We have all branch related courses in first year

It's such a chubby book

No science or stuff like that

Anonymous

4:44 PM

Same here

understanding why a robotics club would assign that as a qualifying problem: ?!?

Anonymous

@Yashas Oo

Anonymous

That sounds bad

I guess it might be testing your ability to research stuff you don't know yet.

@0celo7 dimensions as 'units' or dimensions as 'size of the book'

Anonymous

2 mins ago, by Blue

That's a science club in disguise

4:45 PM

I've never had a copy of Sakurai myself, so

Digital systems, C Pro, data structures, IT workshop (basically how to use Linux and intro to computers), computer systems organisation/arch, etc :P

shrug

Anonymous

@Yashas Oh, we have those from next year onwards mostly. Now we just have C and numerical analysis

Anonymous

One of the professors agreed to teach me theoretical physics...so pretty excited :)

@JohnRennie @Blue Any reference link from where I can learn this stuff in 30 mins?

Anonymous

4:47 PM

@Yashas users.csbsju.edu/~frioux/q-intro/QM-Gas.pdf

Stuff to solve neutron in a box

Anonymous

If you know basic QM it should be very easy

Anonymous

Just watch AK lectures on Youtube for basic QM

Anonymous

That document explains the rest

@Yashas I think this is exactly the point of the question: it was an engineering exam, and therefore the correct answer is what I said above.

4:49 PM

Lol

maybe, maybe not

@Semiclassical size

kk

then i have no idea

Anonymous

@lılostafa I can agree with that. Any "true" engineer would say that the pressure is $0$.

Anonymous

I'm a fake one

4:51 PM

if we use that E ~ V^(-3/2), then that gives P = 3/2 E/V ~ V^(-5/2)

@Blue You'll turn into a real one slowly in your undergrad years, no matter how bad you try to avoid it

in which case you need to know the size of the box to compute the pressure, no?

Anonymous

@lılostafa Noooo ;_;

Anonymous

@Semiclassical Yes

then I doubly dislike the problem. can't quantify it without knowing the size of the box

4:53 PM

@Blue only a mathematician would be afraid of becoming useful.

lol

i think being able to quantify how small something is, is a useful skill

That's basically what analysis is...

Hi chat.h.physics

sure, if you count dimensional analysis :P

Anonymous

iH

4:56 PM

I am preparing an essay on this statement - "Einstein was not only the one of the three godfather of Quantum Mechanics but also the sole godfather of Wave mechanics"

I am collecting points

to write

three godfathers - Einstein , Planck ,Debroglie

Anonymous

Why would you waste time writing essays?

its just an assignment

mmm, early quantum history

Anonymous

Oct 8 at 17:40, by Icemybread

@bolbteppa why does einstein feel like he has the right to say that? what did he ever do in his life anyway?

facepalm

Anonymous

4:59 PM

XD

ow

previously @JohnRennie helped me in explaining many of the Einstein's quotes!

any1 watched the movie "The Life"

some1 was saying its based on space!

@Semiclassical compared to a standard Springer book:

user image

it's an inch wider

same height

shrug

publishing, man

it's a weird world

@Semiclassical do u say "neat" anymore? :)

5:03 PM

occasionally, lol

I suppose the point re: Einstein is him being willing to postulate the existence of quanta of light

that's how he explained the photoelectric effect, for instance

From Planck he got the idea of quanta, but attributing it to light was another step

This all feels rather reductive, though. Early quantum theory history is confusing.

Man I got close to figuring out how to calculate the speed the projectiles need to be shot with to hit a specific area, but I only have one problem now and it's that I can't get the height of the cannon factored in there to hit the same spot regardless of what altitude the cannon is moved to.

This is what I've got so far, it works on leveled plains, i.e. when the cannon is on the same level as the target:

v0 = SQRT((d * g) / sin(2a))
g = 9.81 obviously
a = angle
d = distance
v0 = starting speed

I don't like QM anymore -,-

good

no one should like QM

pfffft

flagged as offensive /s

Anonymous

lol

Anonymous

5:07 PM

olo

Anonymous

ool

Anonymous

loo

@Semiclassical I am trying to set up my home library and Sakurai doesn't fit anywhere

lol

Anonymous

Throw it out

5:09 PM

oh and you'll be monitoring my trash for it, I'm sure

Anonymous

Sure

lately i've been playing around with pilot wave calculations, just out of curiosity for what those look like

@Blue ^

and (proudly) download it from libgen

if you proudly download from libgen, you need to rethink your life

one weird little bit out of that: in general, one can take bound energy eigenstates to have purely real wavefunctions

in which case the probability current is zero

and therefore the velocity in the pilot wave sense is also zero. so such eigenstates would correspond to particles at rest :3

5:13 PM

@0celo7 OK. Throw it out and shamefully download it from libgen

Can someone help me get the height into that equation?

the closest I've seen to an explanation of why that should be true is that "Pilot wave trajectories are not well suited to bound state problems, which are really steady state phenomena."

Anonymous

@Semiclassical Interesting

it does seem like pilot wave theory is more built for understanding scattering problems

which is a bit frustrating, given how much simpler to compute bound states are

the best compromise:

user image

height mismatch but the width forces it

5:19 PM

eh, you could arrange it so that it's decreasing in height away from the wall

Anonymous

All your books look so new and untouched

but that might lose some of the organization

@Blue because I take care of them

my copy of griffiths E&M is literally in pieces :(

Anonymous

@0celo7 Ah, then you'd have a stroke if you see my book shelf

5:20 PM

user image

this one is barely hanging on

oof

my copy of Jackson's E&M similarly hasn't held up well

though I got another copy in better shape to replace it

@Blue I put books in plastic bags when in my backpack so they don't get banged up

I try not to crease paperbacks, etc.

Anonymous

wow

Anonymous

you deserve a medal

you get the books you deserve, really

5:23 PM

it's hard to take care of the pages though

front:

user image

side:

user image

it's washed out there, much darker stains irl

maybe if I read with gloves on...

what I in general avoid doing is writing in books

i'll do it occasionally, but only just

@Semiclassical I correct mistakes and sometimes write a note that will help me if I need to understand something particularly difficult again

Anonymous

I don't feel like I've digested the chapter till I have filled the pages with short notes and pen marks

Anonymous

But that's me

if i ever do write in a book, it's always with pencil

5:26 PM

@Semiclassical correct

Anonymous

I hate pencils

how about using a highlighter

Anonymous

They fade away

@Blue blocked

@BAYMAX gtfo

5:26 PM

^

gtfo?

google

highlighters are for high school children and law students

@Blue You write with pen in your books??

Anonymous

@lılostafa Of course

i wouldn't mind highlighters for printouts of stuff

Anonymous

5:27 PM

I'm savage

La di da

and it does make a difference whether you own the book or not

Anybody here with over 200 IQs?

Anonymous

user image

Anonymous

My books look like this ^

5:28 PM

leave

i don't mind that if you own the book, tbh

very bad

at that point it's yours to do with as you will

Anonymous

Yeah, obviously. I wouldn't do that with a library book

kk

5:29 PM

How do people even destroy books?

burn 'em or pulp 'em

No, like your Griffiths

oh

well, first off

My Straumann falling apart is due to a binding error

griffiths as a book isn't really that well bound

5:30 PM

My Griffiths (E&M) was my only book that totally fell apart

add to that the fact that I kept my copy in my backpack a lot

and therefore it was subject to quite a bit of shearing forces

I have a book pocket in my backpack

it keeps them immobilized

consequently the glue binding the pages together separated into a few pieces

so my copy of griffiths is now really a set of separate bound sections

@Semiclassical Same as mine. But I still keep that copy for historical reasons.

(I bought a new one for someone else and he gave it back after a few years)

i've still got mine at my desk on campus

5:44 PM

@Blue Same here.

Guys, is it unethical/ unacceptable to use pens in books?

Anonymous

wut

Some of my friends to scorn me for that.

Anonymous

Everything is ethical unless it gets you into jail

Any more opinions?

I wonder if people get disgusted to see pens being used on book pages.

Anonymous

I get disgusted seeing people use pencils to write notes

Anonymous

5:50 PM

That doesn't mean my opinion matters to them anyway :'D

It matters to me.

I don't want people to get disgusted.

Anonymous

Aw so sweet

@JohnRennie chicken is cooking

@0celo7 what are you making? The teriyaki? Or was that last night?

@JohnRennie teriyaki

going to serve with rice and stir-fried vegetables

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