0
votes
0answers
40 views

Euler Equation Arbitrary Quantities

I have a question about the Euler equation. For some state I can write down: $$ U = TS - pV + \mu N$$ In this equation $T$, $p$, $V$, and $N$ are directly measurable so they have fixed values. ...
0
votes
1answer
66 views

Difference between heat and work

According to the Kinetic Theory of Matter, temperature is nothing but a measure of the kinetic energy of matter. My textbook says that the change in internal energy of a system is the heat gained plus ...
1
vote
0answers
30 views

Understanding the phase separation of a chemically reactive mixture

Let's consider a mixture of solvent and components $A$ and $B$ such that $A$ can transform into $B$ with a rate $k_1$, and the reverse reaction with a rate $k_2$. $A \rightleftharpoons^{k_1}_{k_2} B ...
10
votes
0answers
165 views

List of known universality classes

I am working with RG and have a pretty good idea of how it works. However I have noticed that even though the idea of universality class is very general and makes it possible to classify critical ...
3
votes
1answer
51 views

Simple estimation of the critical temperature of water

I'm trying to develop fermi estimation skills and I came up with a question for which I don't even know where to start from. Here goes: Is it possible to estimate the critical temperature (say in ...
4
votes
0answers
61 views

Is the stability matrix of a linearised RG flow always diagonalisable?

This is a follow up on "Why are the eigenvalues of a linearized RG transformation real?". My question is simple: Is there some physical (or mathematical) reason for the stability matrix of ...
1
vote
1answer
30 views

Classical limit of non-interacting, relativistic quantum gas (Kapusta/Gale p.8)

I want to understand two equations in "Finite temperature field theory" by Kapusta and Gale on page 8. The partition function is $$ \ln Z = V\int \frac{d^3 p}{(2\pi)^3}\;\ln\left(1\pm ...
0
votes
1answer
38 views

What is the difference between reversible and irreversible adiabatic expansion?

What is the difference between reversible and irreversible adiabatic expansion? Is it true that the work done by the gas is the same but the pressure applied externally differ between two process? ...
2
votes
2answers
130 views

Does entropy have a physical meaning?

Entropy is incredibly useful as a mathematical tool. But what does it actually mean? I understand that the Boltzmann entropy is defined by: $$S=k\ln{\Omega}$$ With $\Omega$ being the multiplicity ...
1
vote
3answers
57 views

When the low temperture reservoir with negative temperture (Kelvin), such as Ising model, is the efficiency of ideal heat engine larger than 1?

The ideal Carnot engine works between two heat reservoir with two temperatures $t_h$ and $t_l$. Its efficiency is then $1-\frac{t_l}{t_h}$ . If the low temperture reservoir is the Ising model with ...
0
votes
1answer
17 views

Is it possible to cool magnetic dipoles with a magnetic static field?

Suppose you have a bath of magnetic dipoles, with a common mean rotational kinetic energy. Now you apply a very strong magnetic field so that the dipoles align with the field, thus "losing" their ...
0
votes
1answer
35 views

compressibility of cold atoms in optical lattices

The compressibility of cold bosons in an optical lattice is defined as $\kappa = \frac{\partial \langle n\rangle}{\partial \mu}$, where $\langle n\rangle$ is the density and $\mu$ is the chemical ...
1
vote
1answer
46 views

MIcrocanonical and Canonical - The thermodynamic limit

Considering a two level system with energies $ 0 $ and $ \epsilon$, we write out the single particle partition function with ease to be, also N-particle partition function for non-interacting ...
3
votes
1answer
99 views

How does statistical mechanics predict that hot air rises?

Does hot air rise -- from a statistical-mechanical viewpoint Question #6329 asks whether and why hot air rises. The consensus answer is straightforward: - hot air is less dense than cold air - ...
6
votes
1answer
124 views

Why do phase transitions even exist? Why not smooth density change curves?

Why do phase transitions even exist? Why not smooth density change curves? What properties of matter, quantum or otherwise, predicts that matter will undergo phases at different pressures and ...
0
votes
1answer
39 views

How can entropic effects be prevalent at low temperatures?

I read in a book that at low temperature the hydrophobic effect (for example) is entropic but at high temperatures it is enthalpic. I thought that entropy should decrease at very low temperatures. ...
0
votes
1answer
63 views

Helmholtz free energy from a relation for entropy

The Legendre transformation defines the helmholtz free energy (at least according to my lectures) as: $F(T,V,N)=E-TS$ It also says to start with $E(S,V,N)$ and $T=\frac{\partial{E}}{\partial{S}}$ ...
3
votes
1answer
69 views

Definition of entropy in nonequilibrium states

Thermodynamical definition of entropy $$S(p)=-\int p\ln p~dx$$ is defined only on equilibrium system. But why can't we use it for non-equilibrium system? Is there a well-accepted definition for it?
1
vote
1answer
37 views

Spontaneity / Free Energy of Non-Isothermal Process

I'm trying to determine a lower bound for the work input necessary to make an entropy-reducing process "spontaneous" in the sense that the 2nd law is not violated. For a constant temperature and ...
3
votes
3answers
289 views

Axioms behind entropy!

The concept of entropy is very ubiquitous, we learn about its uses starting from Information Theory (Shannon entropy) up to its basic definition in statistical mechanics in terms of number of ...
2
votes
2answers
127 views

Who invented the perfume bottle thought experiment?

A common thought experiment used to explain the second law of thermodynamics, the "arrow of time", etc. is perfume escaping from an opened perfume bottle; the perfume is likely to diffuse into the ...
6
votes
9answers
2k views

What is entropy really?

On this site, change in entropy is defined as the amount of energy dispersed divided by the absolute temperature. But I want to know: What is the definition of entropy? Here, entropy is defined as ...
2
votes
2answers
60 views

What materials are used in non thermal plasma?

While reading about non-thermal plasmas, I came across their ionization potentials(~1%), and other capabilities, such as their non Maxwellian energy distributions. At what temperatures, and pressures ...
3
votes
1answer
118 views

Entropy of a two-level system

Consider a two-level system with energies and degeneracies $\epsilon_0 = 0, g_0=1$ and $\epsilon_1 = \epsilon, g_1=4$. I can show that the temperature at which both levels are equally populated is ...
1
vote
0answers
66 views

What algorithms can be used to compute the binodal in a ternary Flory-Huggins theory?

What are the most popular algorithms used to obtain a binodal curve for the ternary mixture (starting from Flory-Huggins theory)? I would like to obtain a plot similar to the one calculated here ...
12
votes
2answers
966 views

Temperature of a neutron star

In our everyday experience termperature is due to the motion of atoms, molecules, etc. A neutron star, where protons and electrons are fused together to form neutrons, is nothing but a huge nucleus ...
0
votes
1answer
47 views

Which function denotes the energy of thermal motion within a system?

In thermodynamics, the heat $Q$ is defined as a type of energy in transfer, and is not a state function, which function denotes the energy of thermal motion within a system? 1) $TS$, (there is a ...
2
votes
1answer
48 views

Why does nuclear matter tend to maximize pressure?

I'm reading a text about equations of state of dense nuclear matter. It is often stated that the phase with maximum pressure is preferred. Why is that?
0
votes
1answer
97 views

Can statistical mechanics explain the second law completely? [duplicate]

Statistical mechanics is restricted to the postulate of the equal a priori probability, but this postulate does not need to be considered for thermodynamics, so the valid ranges of statistical ...
0
votes
1answer
50 views

Thermal Velocity

What is thermal velocity? What is it's physical significance? Wikipedia says: The thermal velocity or thermal speed is a typical velocity of the thermal motion of particles which make up a gas, ...
2
votes
3answers
159 views

Why is Entropy's Definition Useful?

I have somewhat of an understanding for other physical quantities, but as far as entropy goes I only know it to be "disorder". Why is the change in entropy formula an appropriate/useful definition, ...
2
votes
3answers
128 views

Is thermodynamic free energy and potential energy the same thing?

The equation for free energy $F$ and potential energy $E_{pot}$ are: $$ F=U-TS \\ E_{pot} = E_{tot} -E_{kin} $$ But the temperature $T$ is proportional to the average kinetic energy of a system. So ...
1
vote
0answers
72 views

Ergodic Hypothesis; canonical ensemble

I'm currently studying for an exam in thermodynamics/classic statistical mechanics and 2 things came up which are confusing me. First the ergodic hypothesis states that it is equal to take the mean ...
8
votes
2answers
198 views

What conditions do a bunch of atoms need to satisfy to have a temperature?

What conditions do a bunch of atoms need to satisfy to have a temperature? Suppose that we have a beam of helium atoms travelling in a common straight line, equally spaced with the same velocity. If ...
4
votes
4answers
438 views

Mathematical proof of the Second Law of Thermodynamics [duplicate]

Is there some book or paper that formalizes statistical mechanics, like some people have done with relativity, and proves the second law of thermodynamics from more foundational axioms?
0
votes
1answer
58 views

Canonical ensemble, energy, heat bath

I am studying through the book Thermodynamics and Statistical Mechanics by Walter Greiner and I’ve got a couple of doubts when I was reading about the classical ensembles, specially the Canonical ...
4
votes
3answers
117 views

Problems with units of entropy in statistical thermodynamics

The statistical thermodynamics definition of entropy: $S = kN \ln (W)$ troubles me a lot with the problem of dimenstions. where $S$ is entropy; $k$, the Boltzmann constant; $N$ the number of particles ...
4
votes
3answers
212 views

Existence of negative temperatures and the definition of entropy

How negative temperatures can be possible has been treated on StackExchange before (several times in fact), but in light of some recent academic discussion, most of these answers seem to be possibly ...
3
votes
3answers
193 views

In what limit do we *really* get Maxwell-Boltzmann statistics from Bose-Einstein and Fermi-Dirac?

Fermi-Dirac and Bose-Einstein energy occupation number $n(\epsilon)$ in natural units ($[T]=[\epsilon]$) read $$n(\epsilon) = \frac{D(\epsilon)}{e^{(\epsilon-\mu)/T}\pm 1},$$ where $D(\epsilon)$ is ...
4
votes
1answer
181 views

What's the most fundamental definition of temperature?

What's the most fundamental definition of temperature? Is it the definition concern about average energy, number of micro states, or what? By "fundamental", I mean "to be applied" in such general ...
1
vote
0answers
45 views

Free energy a continuous function of temperature but may not be differentiable everywhere?

So according to my understanding, the free energy of the system should be a continuous function of temperature. This is because if the free energy is not continuous at temperature T, then at this ...
4
votes
4answers
184 views

Question on entropy

All of my textbooks mention, that entropy-change of all spontaneous physical, and chemical processes is positive, and that such processes need another condition to fulfill- decrease in the net ...
1
vote
0answers
27 views

Effusion of particles from one box to another - pressure calculation

Suppose we have a container divided into equal halves. Right half is fixed at temperature $T$, volume $\frac{V}{2}$. Initially it has pressure $P_0$, a hole of area $A$ is opened between them. I ...
7
votes
3answers
125 views

What would be non-ergodic physics processes?

As the title says, what would be non-ergodic processes that occur in statistical physics? Many textbooks do not really cover ergodicity really well so I ask this question. I can't suddenly remember ...
1
vote
0answers
54 views

Calculating heat capacity from the equation of state

It is known that within thermodynamics alone, given the equation of the state of a system, one cannot explicitly determine the heat capacity. What is the mathematical reason for this? Intuitively, it ...
1
vote
1answer
65 views

Calculation of the differential of the entropy

In this review (for those who wants a precise reference see page 8 eq 21), the Author says that: \begin{equation*} S=-\sum_{i}P\left(i\right)\ln P\left(i\right) \end{equation*} and using the ...
2
votes
1answer
89 views

Entropy is constant. How to express this equation in terms of pressure and density?

In hydrodynamics of an ideal, non-compressive flow we use 5 variables: pressure $p$, density $\rho$ and velocity field $\mathbf{v}$. So we need 5 equations. Landau's "Hydrodynamics" states that the ...
27
votes
8answers
3k views

Why is absolute zero considered to be asymptotical? Wouldn't regions such as massive gaps between galaxy clusters have temperatures of absolute zero?

Why is absolute zero considered to be asymptotical? Wouldn't regions such as massive gaps between galaxy clusters have temperatures of absolute zero? I just do not see why our model must work the way ...
2
votes
1answer
222 views

Flory-Huggins ternary phase diagram with a neutral component

I am searching the literature for the Flory-Huggins phase diagram with the following components : polymer, solvent, and a third component that does not interact with the other components (just entropy ...
29
votes
7answers
3k views

Homemade salad dressing separates into layers after it sits for a while. Why doesn't this violate the 2nd law of thermodynamics?

The oil, vinegar and other liquids in homemade salad dressing separate into layers after sitting for a while, making the mixture become more organized as time evolves. Why doesn't this violate the ...