/sci/ - Science & Math

Derive the heat death of the universe.

>>12635235
Only works if the universe is an isolated system. In that case, 2nd law says entropy always increases.

>>12635258
Derive the second law of thermodynamics

>>12635267
You can't produce work in a cycle with one heat reservoir.

>>12635258
You’re missing the whole “nothing can happen” part.

>>12635225
Calculate the thermodynamics of the average American's fart, factoring in the shart probability

>>12635280
You're missing the point; once entropy reaches a maximum, nothing CAN happen.

>>12635285
That’s not included in the 2nd law.

Classical thermodynamics or stat mechanics as well?

>>12635225
You should be able to solve this then,

>>12635284
Easy.
- Shart probability of 10%
- Interpolate 10% of the line between the lower heating value of methane (no shart, no moisture) and higher heating value (full shart, lots of moisture).

End result is about 800 kJ/mol.

Average american fart has a volume of 0.3 L = 0.01 moles of air.

So you're looking 8 kJ per fart.

There are about 15 farts of this magnitude per day, so that's (8*15)/(24*60*60) = 0.001 Watts per person.

A Boeing powerplant requires 90,000,000 Watts to fly a plane, so you would need 90 BILLION people to fly a plane with their farts.

In that regard, farts aren't worth thinking about, thermodynamically.

>>12635225
I read somewhere that there is an astronomically low chance that a heated pot of water will freeze instead of boiling. What's that about?

>>12635294
It is included. Once entropy reaches a maximum, everything is at the same temperature, so nothing can happen; that's the Clausius statement of the 2nd law.
>>12635298
All of it.
>>12635306
Yes this is like first grade stat mech. Next step is magnetocaloric refrigeration.

>>12635358
Frank, is that you?

>>12635306
Pretty sure that's a solved exercise in my undergrand Stat Mech textbook.

>>12635341
Just how there's an astronomically low prob that heat will flow backwards, so it never happens. Everything in thermodynamics is an average of all possibilities, and there are SO many possibilities that the average literally always happens.

>>12635225
Is information theory bullshit?

>>12635375
Nope, it's statistics and it's reliable

>>12635358
>Once entropy reaches a maximum, everything is at the same temperature, so nothing can happen
*laughs in reversible process*

>>12635370
>Just how there's an astronomically low prob that heat will flow backwards
How would that work? How would it look on a molecular level? A majority of them align to collide head on and cancel each other's velocity out?

>>12635409
You are correct. But the likelihood of that happening is super small because of all the possibilities, things collide exactly to cancel out.

>>12635427
Wait, molecular velocity is tied to temperature, right? What's heat then?

>>12635330
based

>>12635444
Yeah temperature is like an average kinetic energy. Strictly speaking, heat is something that transfers, not a property like temperature or energy. Heat is the transfer of energy between two things of different temperatures, and it's special compared to other forms of energy transfer because it's the only one that carries entropy.

>>12635427
>>12635444
>>12635466
And this ties directly back to our convo about likelihood of heat flowing backwards or water spontaneously freezing, because in thermodynamics only the most probable things happen, and heat serves as an equalizer of entropy, and the 2nd law saws entropy strives for a maximum. Maximum entropy is therefore the most probable state, which is NOT the situation of velocities cancelling out like you said (because that's one of insanely many possibilities where velocities don't cancel).

>>12635225
Can we use thermodynamics to solve part of the hard problem of consciusness and qualia? Think about this, cosmic microwave background radiation is asymetric, it means there's an external influence on this universe and a problable multiverse. Also if the holographic universe theory is right, then it means consciousness has another source than just causality derived from the big bang, hence all compatibilists metaphysics were right all this time while still showing panpsychism is wrong.
PIC RELATED, I need help.

Hey OP, I want to know something curious and advanced about thermodynamics! Anything goes

>>12635225
explain the difference between galvani potential and chemical potential

>>12635225
Can you explain how the Sommerfeld expansion is done? I can't fucking get it no matter how much I read about it.

>>12635497
>hard problem of consciusness and qualia
no such thing

>>12635737

>>12635225
I like thermodynamics since I like the mix of intuition and rigor, I've been trying to mix my schedule up by throwing discrete dynamical systems into the mix.
Is this path worth it, academically speaking?

>>12635756
Also, what would it mean for the universe to be a closed system? I often think about closed systems as open sets but I don't think that would work since if space is infinitely large and approximately continuous then it'll be like Rn, the probability of shit bumping into each other would most likely reach 0 with boundless expansion.

>>12635225
will the universe repeat again and again forever?

>>12635225
In intuitive or layman terms (don't just state some equation) what is a Legendre transformation?

>>12635797
Not OP, but it basically just lets you analyze a quantity in terms of its derivative. Its utility follows directly from the variation principle, and the principle of least action, where you must minimize the lagrangian as a function of a coordinate and its derivative. It's therefore natural to use a transformation that lets you analyse the derivative (conjugate) function instead.

In the case of thermodynamics, it lets to take a mapping from temperature to entropy, and make inferences on the temperature of a system based instead on its entropy.

>>12635848
So if I have some 4 dimensional manifold that maps temperature I can find an Isomorphism to the entropy at each point or am I getting it all wrong? Can you even talk about entropy in a point?

>>12635225
i know how to violate the first and second laws of thermodynamiccs which guide the forward arrow of time.

>>12635857
Temperature is a Legendre transform of energy

>>12635225
Has thermodinamics been applied to economics?
>t. filthy biochem studying economics

>>12635225
Are you familiar with Schroeder's Introduction to Thermal Physics? If so, what's your opinion on it as an undergrad thermo textbook?

You working on any information theory of thermodynamics?

>>12635225
My friend doesn't think entropy is real...can you give me a detailed explanation of what entropy is and why it's real so I can rub his retarded face in it?

>>12635225
Best thread on sci right now. What's your major?

>>12636413
Also derive specific volume from Gibbs energy.

>>12635225
does heat transfer through materials in a wave-like fashion?
for example, suppose you have a thick sheet of a magical super heat-conducting material, and contained in this sheet is a row of magical hyper-insulation material that does not conduct heat whatsoever. would you see an interference pattern of heat distribution on the other side of the hyper-insulation?
i know literally fuck-all about physics, and i was wondering this the other day

>>12636431
Not op but

Look up how fourier transforms were discovered. They were used to calculate the diffusion of heat down an infinitely long metal rod. Look up the heat equations for more info. I'm unsure off the top of my head what the differential in the insulator heat transfer rate and metal plate. I guess it would because the metal would act like an infinite heat sink stabilizing a wave pattern that is large compared to the total heat transfered making a more detectable signal in comparison.

If I have two parallel plates with a grid of ideal chains connecting them, they will be pulled together through an entropic force. (https://en.m.wikipedia.org/wiki/Ideal_chain#Entropic_elasticity_of_an_ideal_chain))
My question is:
If I make it so that each of those ideal chains is knotted like a trefoil of figure eight knot, how much does this change the force between the plates?
Feel free to make whatever simplifying assumptions you’d like as long as the result has nontrivial dependence on the knot type.

I had a teacher that said something like he himself didn't understand why the concept of enthalpy was even invented and that it wasn't actually needed or something. I'm still not sure what he meant by that. Maybe that we could just treat internal energy and pressure*volume separately without calling it "enthalpy" ?

>>12635225
derive me the formulas for plotting a phase diagram branches from for any possible liquid from some experimental coefficients like Antoine's

>>12635330
based retard

>>12635225
I am a brainlet unable to derive or research the answer to this question, so please spoon-feed the answer: What is the simplest formula for obtaining the black-body emission rate, in watts-per-square-meter, from the temperature of said body in degrees K? And the simplest procedure for calculating a spectral power-distribution from a temperature.

>>12636402
That was one of my first books. I recommend it for undergrads and you'll also have to come back to it later to appreciate some things (especially the chemical thermo parts).
>>12636406
Yup, my research in fluctuation-dissipation has overlaps with information theory.
>>12636410
You and your friend are both correct. Entropy is as real as energy, and both are not "real" in the sense that they can be directly measured, they're only calculated with other measurable quantities. Energy and entropy are concepts that satisfy certain conservation laws (1st and 2nd laws of thermo, respectively). But basically entropy is a measure of the number of possibilities, it's just a statistical concept.

>>12636413
Mechanical engineering.
>>12636416
v = dg/dp for a constant temperature process in chemical equilibrium.
>>12636431
Wave-like transfer occurs in pure crystalline solids only. You can observe this interference you speak of, but only at low temperatures because the waves tend to scatter in a messy fashion with other waves at higher temperature. This is a fascinating area of research anon, you should be proud of yourself. Look into the area of phonon transport and thermal diodes if you want to explore further.

>>12636697
Vibrational energy still transfers in a 1D fashion along the chain, even if it's knotted, unless the knot is so tight that you have interactions with parts of the chain.
>>12637042
Enthalpy is useful in open systems, and the pv part is called "flow work" because it's work put on a control volume due to flowing fluid. It becomes apparent if you derive the 1st law for open systems from a differential. It's extremely convenient and your teacher should be ashamed. See pic attached.

>>12637522
I don't see enthalpy on your pic related either. Also the guy was a PhD student and was extremely smart from what I could tell. It was just a half sentence he mentioned as an aside that they invented enthalpy but it doesn't actually make sense or something but now they have to roll with it because of conventions n shit. I've been trying to make sense of it since.

>>12637240
Clausius-Clapeyron is a good start
>>12637480
Use the Planck distribution, then integrate over the spectrum to get the Stefan-Boltzmann law.

>>12637551
My pic is an energy balance due to flow work only. If you include internal energy of the fluid, you end up with a quantity u+pv. Instead of writing u+pv all the time, why not just write h=u+pv?

>>12637554
thanks, I will try
Do you also know a easy algorithm to plot a Txy binary component diagram without requiring massive iterations? Pxy is easy but Txy is a challenge, asked to many people but nobody knew how to answer.

>>12637551
Also think of chemical reactions, where enthalpy change is used all the time. When you light a fuel such as natural gas, the gas+air mixture expands rapidly and changes volume, but the surrounding atmosphere puts a pressure on your little experiment. So the combustion volume does work on the atmosphere, and that's the "pv" term in h=u+pv. Now an energy balance says Q = change in "u+pv". When people measure the heat of combustion Q, they're actually measuring change in "u+pv". It's much easier to just write change in "h".

>>12635225
How does it feel being dumber than a math undergrad?

>>12637690
Feelsbadman. But my choice of study brought me closer to my goals in engineering, not supreme intelligence.

>>12637554
Very nice. That's a lot simpler than I expected once the pesky unit-conversion is supplied like that.

>>12635225
Ok, I'll bite.
What is the PDE that describes the pdf of a noisy logistic stochatic process?

>>12635225

Compute the thermodynamics of a basic chemical reaction, say H+H - - > H2, but from first principles

>>12637505
>That was one of my first books
...Dr. Schroeder, is that you?

>>12635225
Hello
Can you give a simple compare and contrast between the following values:
>entropy
>exergy
>gibbs free energy
>there was another but I forgot its name

>>12637512
>phonon transport
holy FUCK i'm a retard. see, i originally started thinking about this because i had learned about the concept of phonons, as in describing sound waves as lightwaves, and was absolutely fascinated by this metaphenomena, i wondered if you could come up with a similar description for thermodynamic energy transfer.

but obviously those would still be phonons, since phonons are just the displacement of matter, which would be the mechanism of how heat travels through materials. i feel very silly to have not figured this out on my own. unfortuantely i have too many interests already, so thermodynamics is low on the list of things to study, but it's definitely on that list, i'll get around to it someday

>>12635514
The equations of motion describing atoms and molecules moving are time reversible but the macroscopic effect of heat, which is also atomic/molecular movement, is not reversible. This is called Loschmidt's paradox, and has sparked debates about the arrow of time among retards, but the fluctuation theorem explains it nicely.

>>12635225
There is bit of chemistry there but from a thermodynamics point of view,
OP, Do you think that plasma electrolysis of water would be more efficient and could be done without degradation of the apparatus ? (compared to KOH electrolysis,the cell degrade over time).

basically I would use superheated dry steam injector to raise the thermal energy of the steam, and then push the steam over a tungsten air gap with arcing going on it.

I would need at least around 1MJ per mol of energy to fully dissociate water. probably more for the plasma not to recombine instantly.

Then past the jet, a strong electric field from two plates would separate the species.
Since the protons and oxygen ions have different weights and charges, their beams would follow a different trajectory until their energy drops and they recombine (getting neutral again) up to a collector.

How can i tackle this problem, supposing a constant flow of steam at stable temperature, speed, pressure and temperature, and an equilibrium pressure and temperature of the vessel (adiabatic conditions), Where the inflow equals outflow...
This would be done inside the vessel with an excess of dihydrogen or dixogyen.
The arc would be probably an RF microwave arc so that the ions are not pushed toward the arc electrodes.

>>12639269
I see OP was bullshitting and doesn't know anything about stat mechanics.

>>12639269
The Fokker-Planck equation.
>>12641412
I know everything about stat mech.

>>12640584
>Entropy
A measure of the number of possible states (ways to distribute energy). Unlike exergy and G, it has units of J/K. If you multiply change in entropy by temperature, this gives you the heat absorbed by the system.
>Exergy
This is the change of Gibbs free energy, where the change is referenced from the surroundings or atmosphere, because the max amount of work you can extract from a system occurs when it has achieved equilibrium with the surroundings. This has entropy in it, because change in entropy times temperature is the reversible (max possible) heat transfer.
>Gibbs free energy (G).
Like entropy, this quantity is only meaningful when you calculate a difference between two states. Like exergy, the difference in G between two states is the max possible work at some pressure and temperature. You often see this used for chemical reactions and batteries, because ideally these things won't change pressure or temperature when operating.

>>12635225
What is the most efficient way to produce heat?

>>12641555
A heat pump, which is a refrigerator running in reverse. Yes, it's more efficient than dissipating electricity.

>>12635280
No he didnt

Have you seen the conspiracies about the pyramids and ancient technology? Do you think they could be some sort of tesla tower type electromagnetic field generating device? Everyone talks about varying voltage as you go up the atmosphere and the magnetic field of the earth and a million ways old buildings supposedly used those, but nobody can explain how the energy gradient is actually used or the alternating current is formed to create the pulsing that the field needs.

The lost history aspect of this is very believable to me, but I know almost nothing about thermodynamics and apparently know more than everyone I've seen talk about this ever.

>>12637505
Why do you use the order/disorder explanation of entropy instead of the useable energy gradient explanation?

>>12641924
Pic related, the answer is engraved on Boltzmann's grave, and it is the only definition of entropy from which all others follow.

kill urself u inbred faggot

>>12635409
Quick math bit to help make sense of this "astronomically low" thing.... Pick a random rational (or even real) number between 0 and 1. Now it's possible that you pick exactly 0.5, but "astronomically unlikely" since there are many more numbers to choose instead of 0.5. So unlikely in fact that the probability is 0. That's not rounding down, the probability is exactly 0. It's still a possibility, but there's a 0% chance of it happening.

>>12641339
Basics od Plasma physics by Paul M Bellan seems the way to go.

>>12635225
gimme a good book to learn thermo from