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sethoflagos

Youtube says the 2nd Law is Broken.

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23 minutes ago, studiot said:

Does this make it any clearer?

In each pair of cases which do you think is the more difficult task?

Yup and Synthesis, respectively.

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14 minutes ago, sethoflagos said:

Yup and Synthesis, respectively.

Now here is a thermodynamic question that all the textbooks in world will nothelp you with.

However, even though (climate) conditions in Lagos mean you probably never experience this problem, as an experienced enginner, you may well be able to suggest a good way forward.

 

When casting concrete in cold weather the concrete will suffer terminal damage if allowed to freeze in the first 24 hours.

Suggest countermeasures to avoid this.

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My textbooks may be in Lagos, but I'm not : we've been stranded in Holland since February due to the COVID19 restrictions. Hence I've now the time to research some topics I've left sitting on the shelf for a rainy day.

I fail to see the relevance of concrete pouring here. 

9 hours ago, studiot said:

You might also like to look into what Mandl   (Manchester Physics series Statistical Physics) about your youtube issue.

I think (please confrim or correct) that this is a description of it in his introduction to the second law.

He goes on to split the probability function into two functions by , not the states themselves, but of the size of the fluctuations as a result of the N or n.

He shows how the smaller N is the larger the expected fluctuations are from 'equilibrium'.
 

Fluctuations sizes for a single particle are 'off the scale'

secondlaw2.thumb.jpg.f263dfeedfca80954577a891f25e610e.jpg

 

 You've been adding bits and pieces to your postings!

Yes, the Mandl example is representative of the OP. And I have much the same issues with it, at least in the set up.

1) Between state a) and state b), the centre of mass of the gas has moved L/4 from its original position where L is the width of the box. This requires external work i) to set it in motion ii) to stop it again. We'll leave aside the compression element (insufficient info to evaluate) but that issue remains open.

2) In state b) the gas is acted on by a reaction force P*area from the left hand wall that is only opposed by the acceleration forces of the gas towards the right hand wall (at sonic velocity!). It's internal energy being converted pro rata to bulk kinetic energy. At the right hand wall, the reverse happens (KE back to U) until the gas CoM is L/4 to the right of origin and the gas is stationary again. And now, in the absence of frictional forces, we have a simple undamped harmonic oscillator. The gas will NOT "very rapidly ... return to the uniform state of Fig. 2.1(a)" as Mandl states, rather it will remain in an eternal ping-pong state cycling between expansion and compression. Just as it is impossible to leave this cycle without introducing new external inputs, how can it be less impossible to enter it?

I really don't know how Mandl proceeds from these initial premises, but it doesn't appear to be a great start. 

There's more. A lot more. But until we're straight on 1st Law constraints, these examples have nothing to say on the 2nd. 

We seem to be going backwards.

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FYI

How long is "enormously long compared to the age of the universe"? A trillion years for a 1m cube initially at stp?

Well let's rescale. For a 1mm cube this reduces the timeline by a factor of 10^9 ie once in a millenium.

So within a km^3 of the earth's atmosphere (a 10^18 scaling factor), the frequency of events is over 30 MHz.

Back-of-an-envelope tells me that expansion of 0.5 mm^3 @ 2 bar into 0.5 mm^3 of vacuum releases oto 60 microJoules.

2 kW of acoustic energy is rather a lot. If it came from a point source half a kilometer away, that's still ~0.3 microWatts / m^2 which would interfere with normal conversation. And the same sound intensity level is coming from all directions, no matter where you are. 

And of course, we're only considering the most extreme events. Lesser events presumably occur far more frequently yet with still comparable energy outputs. We would all be deafened by the noise!

 

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10 hours ago, sethoflagos said:

 

Yes, the Mandl example is representative of the OP. And I have much the same issues with it, at least in the set up.

1) Between state a) and state b), the centre of mass of the gas has moved L/4 from its original position where L is the width of the box. This requires external work i) to set it in motion ii) to stop it again. We'll leave aside the compression element (insufficient info to evaluate) but that issue remains open.

You need to go back and study first-semester physics. No work is necessary. 

 

 

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2 hours ago, swansont said:

You need to go back and study first-semester physics. No work is necessary. 

So that long walk off a short pier shouldn't exhaust you :-)

There is a difference between 'arbitrarily small' and 'zero'. 

But compression is by far the larger work issue, and this most definitely is NOT arbitrarily small. Even isobaric compression requires 0.5 PV Joules of external work. That's oto 20% of its initial internal energy for heaven's sake. This rises to W = ln(2) PV (=0.7 PV) for isothermal compression; and a minimum of  W = ((2^0.4 -1)/ 0.4) PV (= 0.8 PV) for adiabatic compression of a diatomic gas; W = ((2^0.667 -1)/ 0.667) PV (= 0.88 PV) for the monatomic case. 

This is the source for the 'explosive' energy release when you relax your constraint and allow the gas to undergo free expansion back to its original state. Only it can never find its way back to its original state because it has no mechanism to get rid of its bulk kinetic energy other than by recompression. 

This puts the lie to Mandl's case that "it would only last a very small fraction of a second". No, we are now engaged in fast, real-time energetic dynamics that are well-understood. Your steady accumulation of 'zero work' over countless eons has led to the paradoxical situation that you cannot now return to the original equilibrium state other than by precise reversal of the process that got you there. A process that you have already stated takes far longer than the age of the universe. 

Mandl's Fig. 2.1 (a) is a really good starting point for testing wacky ideas, because it is by definition a perpetual motion machine of the third kind. The slightest (and here I do mean arbitrarily small) nudge in the wrong direction turns it into either a perpetual motion machine of the second kind breaking the 2nd Law, or a perpetual motion machine of the first kind breaking the 1st Law.  

Which kind of wacky are you wishing to defend?   

 

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7 minutes ago, sethoflagos said:

But compression is by far the larger work issue, and this most definitely is NOT arbitrarily small

Before this degenerates into another slanging match, let me step in here.

Seth, you are mixing up macroscopic mechanical theory and microscopic kinetic theory.

This link is proper statistics, you cannot 'mix and match' formulae from macroscopic and microscopic theory without doing this.

No one is suggesting that in Mandl's diagram the system passes directly from state a to state b or from state b to state a.

Either way the change is a gradual process, although there is a vast different of timescale between a to b and b to a.

 

Consider first b to a

There must be a first molecule that leaves side A and moves into side b

Followed by a second, third  and so on, although sometimes and sometimes only , two or molecules will exit the gap simultaneously.

So , however fast or slow, the system must leave state b a bit at a time and move, a bit at a time, towards state a.

A similar deduction may be made for the reverse process a to b.

 

Now statistically the more particles there are the harder or less likely it is for most (all) of them to move from one side to the other, at or near the same instant.

 

Your centre of mass argument is also suspect

My single particle example negates that as its COM is always moving, but by Newton's laws, zero work is being done.

 

 

Finally  I said that Mandl's example was presented in his introduction to the second law.

Like all good courses and texts he is up front about the difficult cases, where the simple theory is insufficient, but I also said he treats this later.

 

 

 

 

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20 minutes ago, studiot said:

Seth, you are mixing up macroscopic mechanical theory and microscopic kinetic theory.

This link is proper statistics, you cannot 'mix and match' formulae from macroscopic and microscopic theory without doing this.

On the contrary, it is you who is attempting to extend some unspecified microscopic action to an unspecified macroscopic effect.

I know that my formulae work for macroscopic systems. You are the one making the extraordinary claim that they are somehow inappropriate so please demonstrate (with numbers!) why my formulae don't work or withdraw your objections to them.

 

THESIS:

50 minutes ago, studiot said:

Your centre of mass argument .....

ANTITHESIS:

52 minutes ago, studiot said:

... is also suspect

SYNTHESIS:

Replace the box with a sphere of the same volume, and have the particles converge radially inward to occupy a concentric sphere of half the volume. The principle of the OP is perfectly preserved and the CoM issue goes away. The compression issue remains. Even Mandl invoked a piston to prepare Fig 2.1(b)

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2 hours ago, sethoflagos said:

So that long walk off a short pier shouldn't exhaust you :-)

There is a difference between 'arbitrarily small' and 'zero'. 

But compression is by far the larger work issue, and this most definitely is NOT arbitrarily small. Even isobaric compression requires 0.5 PV Joules of external work. That's oto 20% of its initial internal energy for heaven's sake. This rises to W = ln(2) PV (=0.7 PV) for isothermal compression; and a minimum of  W = ((2^0.4 -1)/ 0.4) PV (= 0.8 PV) for adiabatic compression of a diatomic gas; W = ((2^0.667 -1)/ 0.667) PV (= 0.88 PV) for the monatomic case. 

There’s no compression. You keep trying to recast this in terms of some other (probably familiar) problem, which is why you don’t end up at the answer in the book. (which is what my earlier explanation was trying to highlight - no compression needed for the one-ball case.)

But I was responding to your claim that work is required for the gas CoM to change, and that’s not the case (the container has mass), which is something one is expected to learn in first-semester physics. Your objection has no basis in physics.

 

1 hour ago, sethoflagos said:

The compression issue remains. Even Mandl invoked a piston to prepare Fig 2.1(b)

But that’s not all he said. He invoked it if you were preparing that state, as opposed to a spontaneous fluctuation. He made a clear (IMO) distinction.

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Posted (edited)
1 hour ago, sethoflagos said:

Even Mandl invoked a piston to prepare Fig 2.1(b)

I had hoped we had returned to more normal forms of discussion.

Since that is not the case I will leave you with the suggestion.

Get a good English (or better Thermodynamic) Dictionary and look up the words 'piston' , which Mandl did not use, and 'partition', which he did.

Both word have very particular and carefully defined meanings.

 

go well and enjoy your stay in the Netherlands  - I find it a very nice place.

Edited by studiot

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Posted (edited)
47 minutes ago, swansont said:

There’s no compression. You keep trying to recast this in terms of some other (probably familiar) problem, which is why you don’t end up at the answer in the book.

"There are an infinite number of possible paths from an initial point to an end point in a process. In many cases the path matters, however, changes in the thermodynamic properties depend only on the initial and final states and not upon the path." - Philip E. Bloomfield, William A. Steele, "Thermodynamic processes," in AccessScience, ©McGraw-Hill Companies, 2008

Do you understand and accept this principle?

If it were so, you would see that the path I choose to take from state A to state B is irrelevant. Obviously, I pick a sequence of paths that are analytic. 

28 minutes ago, studiot said:

Get a good English (or better Thermodynamic) Dictionary and look up the words 'piston' , which Mandl did not use, and 'partition', which he did.

"Of course, one can especially prepare the system to be in this state; for example compressing the gas into half the space and inserting a partition" - Franz Mandl, "Statistical Physics, 2nd Edition", ISBN: 978-1-118-72343-2, June 2013

What compressed the gas? The partition?

You are prevaricating with ad hominem trivia. Seems to be an established habit on this site among some.

26 minutes ago, sethoflagos said:

"There are an infinite number of possible paths from an initial point to an end point in a process. In many cases the path matters, however, changes in the thermodynamic properties depend only on the initial and final states and not upon the path." - Philip E. Bloomfield, William A. Steele, "Thermodynamic processes," in AccessScience, ©McGraw-Hill Companies, 2008

Do you understand and accept this principle?

If it were so, you would see that the path I choose to take from state A to state B is irrelevant. Obviously, I pick a sequence of paths that are analytic. 

 

Edited by sethoflagos
sp

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3 hours ago, sethoflagos said:

"There are an infinite number of possible paths from an initial point to an end point in a process. In many cases the path matters, however, changes in the thermodynamic properties depend only on the initial and final states and not upon the path." - Philip E. Bloomfield, William A. Steele, "Thermodynamic processes," in AccessScience, ©McGraw-Hill Companies, 2008

Do you understand and accept this principle?

We’re not talking about a process. We’re talking about the possible configurations that make up one state. Statistical mechanics, not classical thermodynamics.

 

3 hours ago, sethoflagos said:

If it were so, you would see that the path I choose to take from state A to state B is irrelevant. Obviously, I pick a sequence of paths that are analytic. 

"Of course, one can especially prepare the system to be in this state; for example compressing the gas into half the space and inserting a partition" - Franz Mandl, "Statistical Physics, 2nd Edition", ISBN: 978-1-118-72343-2, June 2013

Do you understand why he says “of course” here? To separate this from the previous sentence, where he talks about spontaneous change. Because they aren’t the same thing.

 

 

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23 minutes ago, swansont said:

We’re not talking about a process. We’re talking about the possible configurations that make up one state. Statistical mechanics, not classical thermodynamics.

Do you understand why he says “of course” here? To separate this from the previous sentence, where he talks about spontaneous change. Because they aren’t the same thing.

It became quite clear after the first dozen or so posts to this thread that the insight I was looking for to answer the OP was not going to emerge.

However I am actually quite grateful for this relentless exercise in mudslinging at my methodologies that you and your partner in crime have been engaged in over the last few days. They're not often questioned when employed in my professional activities, but there's always the chance that they might be and it's as well to be forewarned what arguments might be presented, whether these arguments have any significant validity, and what the most effective counter-arguments are.

So thanks for that.

As things stand, I'm learning more from those who are not posting and could, than from those who are, so as I've made all the points I felt like making and you're just arguing for the sake of it, perhaps it's time to draw this process to a close?

Rhetorical question. You're not obliged to respond.  

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