2
votes
1answer
27 views

Temperature of a neutron star

In our every day experience termperature is due to motion of atoms/molecules etc. A neutron star, where protons and electrons are fused togather to form neutrons, is nothing but huge nucleus madeup of ...
0
votes
1answer
31 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
46 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
79 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
32 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, ...
1
vote
3answers
141 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
74 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
52 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
155 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
284 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
37 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 ...
3
votes
1answer
47 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 ...
3
votes
3answers
160 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
131 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
159 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
38 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
153 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
17 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
107 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
25 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
63 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
68 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 ...
1
vote
1answer
140 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 ...
1
vote
2answers
141 views

Is there an equation to calculate the average speed of liquid molecules?

I seem to remember from first year physics that we can calculate the RMS speed of a stationary, ideal gas with $v=\sqrt{\frac{3RT}{M}}$. Does a similar equation exist for liquids?
8
votes
2answers
257 views

Chemical potential in Thermodynamics

In many scenarios, on computing the partial derivative of the internal energy (U) with respect to mole number (N) is negative. This implies that adding more moles of the substance decreases the U of ...
0
votes
0answers
40 views

Landau free energy

I am reading the statistical mechanics by Pathria in Chap 12. I have a question about the Landau free energy. What is the physical reasoning for that the free energy could be a functional of the order ...
5
votes
2answers
113 views

In thermodynamic systems why must the free energy of the system be minimized?

Is this somehow a consequence of the second law of thermodynamics?
3
votes
3answers
214 views

Is there an upper limit to temperature in thermodynamics or statistical mechanics

In many presentations of statistical mechanics where we have a system of particles having mass, such as the molecules of an ideal gas, the temperature is often equated to the average relative velocity ...
8
votes
1answer
112 views

What precisely does the 2nd law of thermo state, considering that entropy depends on how we define macrostate?

Boltzmann's definition of entropy is $\sigma = \log \Omega$, where $\Omega$ is the number of microstates consistent with a given macrostate. If I understand correctly, this means that it only makes ...
11
votes
2answers
377 views

Quantum entaglement and the arrow of time

I have seen several claims to that quantum mechanics is required to explain the arrow of time which I take to mean the macroscopic irreversibility of physical systems. This is presumably to resolve ...
1
vote
0answers
59 views

Chemical potential of photons [duplicate]

Why do photons have zero chemical potential and what is its the physical significance? From what I know the chemical potential could be interpreted as the energy per unit particle that is put into a ...
2
votes
1answer
100 views

Thermodynamics, chaperones : How to model polymer fragmentation

Living polymers are well described by equilibrium statistical physics. Now I would like to consider a case were living polymers undergo fragmentation due to chaperones. I can think of a kinetic ...
2
votes
1answer
102 views

Quantum Fourier Transform and Entropy

QFT is a nonlocal unitary transformation and so can generate entanglement in a system. It means a separable pure state can be converted into an entangled pure state. Now since the presence of ...
0
votes
2answers
44 views

Is there an analogue to the role of vapor in liquids and gases, but for solids and liquids?

It seems common for an ordered phase to have some amount of disorder present. For example, the average moment of a ferromagnet is less than maximum except at T=0 due to the presence of fluctuations. ...
4
votes
1answer
80 views

A real gas with gravitation-like interaction

Consider a system (a gas) of point-like particles with a gravitation-like interaction (potential) $V(r) \sim \frac{1}{r}$ between pairs of them. One can rule out statistically that two particles will ...
8
votes
5answers
124 views

How can point-like particles in an ideal gas reach thermodynamical equilibrium?

Having learned that the particles of an ideal gas must be point-like (for the gas to be ideal) I wonder how they can reach thermodynamical equilibrium (by "partially" exchanging momentum and energy). ...
0
votes
0answers
20 views

What is Fermi energy and Fermi level? [duplicate]

What is meant by Fermi level and Fermi energy? And what is the difference between the two?
9
votes
2answers
232 views

Nonequilibrium thermodynamics in a Boltzmann picture

The Boltzman approach to statistical mechanics explains the fact that systems equilibriate by the idea that the equillibrium macrostate is associated with an overwhelming number of microstates, so ...
8
votes
3answers
631 views

Why must the particles of an ideal gas be point-like?

Why is a gas of elastically colliding hard balls of finite size not ideal? Respectively: Why is it essential that the particles of an ideal gas are point-like? Especially: Which ...
1
vote
2answers
82 views

System in mechanical but not thermal equilibrium

Let's say there are two systems which can interact by a moving wall but cannot exchange heat. Then the system will be in mechanical, but not necessarily in thermal equilibrium. The maximality of ...
6
votes
3answers
206 views

Why is the Gibbs Free Energy $F-HM$?

With magnetism, the Gibbs Free Energy is $F-HM$, where $F$ is the Helmholtz Free Energy, $H$ is the auxiliary magnetic field, and $M$ is magnetization. Why is this? Normally, in thermodynamics, we ...
2
votes
1answer
85 views

Lennard-Jones induced pseudo-molecules

It can be shown that the Lennard-Jones potential - which describes the interaction between particles in non-ideal gases - gives rise to pseudo-molecules: after a triple "collision" of three ...
3
votes
2answers
386 views

Physical significance of negative temperature

I read some answers regarding negative temperatures but I think my question is new. I want to know that what is the physical significance of negative temperature. Suppose I say a body has ...
1
vote
1answer
143 views

Understanding collision terms in Boltzmann equation

I am reading a paper that deals with the Boltzmann equation. They add a collision which is supposed to account for collisions which happen when particles are within a radius of $d$ from each other. ...
3
votes
1answer
117 views

What is the resolution to Gibb's paradox?

This question is essentially a duplicate of Gibbs Paradox - why should the change in entropy be zero?. The question concerns the following situation: I have some gas of identical particles and they ...
0
votes
1answer
68 views

How do we know that the Virial Expansion exists?

How do we know that the Virial Expansion exists? How do we know that we may always write $\frac{p}{kT}$ as a power series in $\frac{N}{V}$? That is, how do we know that there exists $B_{i}$ so that ...
0
votes
1answer
71 views

Why is $B(T)\approx b(T-T_C)$ near critical point $T_C$ in Landau theory?

In Peskin&Schroeder page $270$ equation $(8.4)$ you see that they approximate the function $B(T)$ near the Curie temperature as $$B(T)\approx b(T-T_C)$$ i.e. they omit $B(T_C)$ in the Taylor ...
0
votes
1answer
61 views

Law of equipartition

Law of equipartition predicts the heat capacity of gases correctly. It assumes that inter-molecular attraction in gases is negligible (which is true). But for solids, inter-molecular attraction is not ...