I understand that Man has math methods to calculate flow networks, but real material systems don't know any math yet they get the right answer anyway! How? What deeper laws of thermo-physics governs this behavior? It is like a Maxwells Demon is operating here... tuning each and every branch flow...
Sorry if this is the wrong place to post, but my inquiry spans so many STEM disciplines I figured I would post it here. Also, I have really looked for papers which address this issue and hope someone on PF can advise.
Given a flow network, which could be any connected set of N resistors, or...
Further consideration - we may indeed have two Carnot engines in "thermal series" but they may or may not be in "mechanical series". If the "work output shafts" of the two Carnot engines are not mechanically connected, then the total output work is indeed Wa + Wb, but if the shafts are...
Agreed. I think my confusion derives from conflating "thermal series" with "mechanical series".
In the above we are connecting Carnot engines in both thermal series and mechanical series. This is a different case from where two Carnot engines were connected in mechanical series but operate in...
Thank you again. That is what Jaynes said. My assumption was that the (combined) efficiency of two engines in series would be = the product of the (separate) efficiencies of each engine, which would always be less than the 1-3 efficiency. But apparently (because of zero net entropy?) that is...
This has been discussed in a previous thread https://www.physicsforums.com/threads/efficiency-of-two-carnot-engines-in-series.173879/
Th conventional answer is that the series efficiency is the same as one engine running between T max and T min but I am skeptical.
I have attached my...
Alright, I will restate the question without using the word gradient - it's the same question:
What then is the "heat death" of the universe? My understanding of the "heat death" is that condition reached where all of the thermal energy in the universe has (spontaneously) diffused to the limit...
What then is the "heat death" of the universe? My understanding of the "heat death" is that condition reached where all of the thermal energy in the universe has (spontaneously) diffused to the point where there are no more (= zero) thermal gradients anywhere - all thermal energy has diffused to...
Boltzmann predicts that a non-zero range (= distribution, = gradient) of particle energies will persist "forever" in the steady-state. Since this is an energy-diffusion process, why do the particle energies not "diffuse" to a single uniform value for all particles the same way a solute/solvent...
I (mechanical engineer) have researched this question but can't get to an answer.
The equilibrium condition for confined particle diffusion of a solute in a solvent is reached when the solute spatial density is uniform (= zero density gradient), and entropy is max.
But per Boltzmann, when...
I think MB applies only to constrained particles which are at a density high enough to exchange kinetic energy. Because if they were not close enough, they could not exchange energy by collision and their initial energy distribution would be maintained and could not devolve to an MB...
Well that is amazing. Thank you all for assisting me. I will continue to work on my understanding of this.
But this leaves another problem - where does "micro" end and "macro" begin? Surely the laws of physics cannot be a function of scale.
So what Boltzmann is saying is that the total energy E of a set of confined particles under adiabatic conditions will continuously share the same E among themselves, and the "most likely" distribution of E is the Boltzmann Distribution? And never a uniform distribution?
And this energy transfer...