Questions tagged [thermodynamics]
Covers the study of (mostly homogeneous) macroscopic systems from a heat/energy/entropy point of view. Consider also using tag: [statistical-mechanics].
2,787
questions with no upvoted or accepted answers
3
votes
0
answers
137
views
Are the force frequencies the same in the discrete and continuous case?
Let's say I have an ideal gas of particles and the strike zone of area $\sigma=\pi d^2$ of a molecule of the molecule is what is the sub system considered. The end of the face of the cylinder is the ...
- 1,045
3
votes
0
answers
70
views
Confusion about Boltzmann distribution
It is well-known that the Boltzmann distribution is given by $p\propto e^{-E/kT}$, where $E$ refers to the energy.
A standard textbook problem is to find the pressure variation in a rotating cylinder ...
- 333
3
votes
0
answers
61
views
Van der Waals equation in PT coordinates
Can Van der Waals equation be meaningfully interpreted in PT plane? Are there modified versions of this equation, which would allow correctly reproducing the liquid-gas separation curve with a ...
- 55k
3
votes
0
answers
57
views
Is a perfect insulator a reality
I recently came across this article:
A perfect insulator, or a material that reflects heat while absorbing none of it, has been created by scientists at the Massachusetts Institute of Technology and ...
3
votes
0
answers
43
views
Burning a match in a one-exit tunnel (or Heavy Rain trial of the butterfly scene)
If you light a match in a narrow labyrinth tunnel where there is only one way the air is coming from, will the flame of a match bend in that direction?
In other words, I want to know if the trick one ...
- 31
3
votes
1
answer
51
views
Can an evaporating black hole emit protons with an energy beyond the GZK limit?
There are protons reaching the earth with energies that exceed what their interaction with the cosmic microwave background should allow.They exceed the so-called GZK limit.
GZK Limit
Could an ...
user353451
3
votes
1
answer
110
views
Cosmological perturbations and energy in an expanding universe?
I was reading an interesting book from cosmomogist Viatcheslav Mukhanov Physical Foundations of Cosmology and I had a specific question about it:
It is usually said that energy conservation is ...
- 1,528
3
votes
0
answers
79
views
Differential geometry and the $P \vec A= \vec F$ equation?
How does one write
$$\vec F = P \vec A$$
(where $\vec F$ is the force. $P$ is the pressure and $\vec A$ is the area) in the language of differential forms? I'm confused cause $\vec F$ is a one form ...
- 1,045
3
votes
0
answers
229
views
Do first-order phase transitions necessarily imply hysteresis?
As an example of first-order transition with hysteresis, I am thinking of the magnetization of the subcritical Ising model as a function of the magnetic field. Or density in the liquid-gas transition ...
- 33
3
votes
1
answer
276
views
Why is the change in energy between products and reactants equal to the heat of reaction?
Suppose we have an infinitesimal process in which reactants are converted to products. Let the variables $N_i$ represent the particle numbers of each of these molecule types, and the energy and volume ...
- 942
3
votes
0
answers
53
views
How negligible is a term in the internal energy for the equipartion theorem in classical mechanics?
The equipartition theorem is a well-known result of classical statistical mechanics, and it states that if the Hamiltonian of a system can be written like this:
$$H=\sum_{j=1}^m {\alpha_j\ {x_j}^2}$$
...
- 31
3
votes
0
answers
213
views
How practical is the Landauer limit to actual computing (including distant future)?
Landauer's Principle is often presented as a fundamental limit of efficiency for classical computing. It states that in order to erase one bit of information, at least the following amount of heat has ...
- 301
3
votes
0
answers
218
views
Entropy - can we express number of microstates as a function parameterized by degrees of freedom?
In some of the answers and comments from this question people contended (not in so many words) that because entropy is parameterized by number of microstates $\Omega$, and the definition of $\Omega$ ...
- 12k
3
votes
0
answers
83
views
Canonical Invariance in the Context of Thermodynamics of the Quantum Harmonic Oscillator
I'm reading a paper titled "Thermodynamical analysis of a quantum heat engine based on harmonic oscillators". Section $C$, is dealing with a subject called "Canonical invariance". ...
- 375
3
votes
0
answers
174
views
What's wrong with the Maxwell demon? Seems very trivial consequence of the second law of Thermodynamics...?
Maxwell Demon's Paradom: The entropy production of the system $X$ becomes negative:
$$\Delta S(X) + Q_X \leq 0$$
Exorcism of the demon:
I believe that this paradox has been resolved by an inequalities ...
- 93
3
votes
0
answers
118
views
Do finite sized 1D Hamiltonians have free energies which are analytic everywhere in the complex plane?
It's well known that 1D classical and quantum short-ranged Hamiltonians have free energies which are analytic/holomorphic everywhere as a function of inverse temperature $\beta=1/k_BT$ (see Araki, &...
- 637
3
votes
1
answer
151
views
View factor in concentric spheres
Consider a hollow sphere $A$ of radius $1$, containing a concentric sphere $B$ of radius $r < 1$. I am trying to calculate the view factor $F_{A \rightarrow B}$, but different approaches give me ...
- 1,401
3
votes
0
answers
209
views
The volume of black hole using Parikh's geometric definition
It is mentioned in this paper (by Parikh) that the volume of stationary black holes can be computed through a geometric definition, which (I think) is not common in literature. The definition of ...
- 4,500
3
votes
0
answers
67
views
Pressure jumps by $2\sigma/R$ across a curved liquid surface. Do temperature and chemical potential have similar jumps?
We know that pressure under a curved surface of a liquid experiences a jump due to surface tension. One of the ways to derive this fact is through a thermodynamic argument. I was trying to apply a ...
- 2,575
3
votes
0
answers
94
views
What is the formal definition of a macrostate?
In thermodynamics, and in particular with regards to entropy, we talk about different microstates giving rise to the same macrostate, that is the same gross overall features. This informal definition ...
- 924
3
votes
0
answers
91
views
Do we have to treat ideal gas as identical particle?
In Quantum Mechanics 2nd edition by Griffiths, he says we can get Maxwell-Boltzmann distribution as we deal with distinguishable particles. And I think ideal gas follows MB distribution; therefore, I ...
- 31
3
votes
0
answers
231
views
Equipartition and coupled harmonic oscillator system
This question has to do with analyzing how equipartition sets in for a system such as a coupled harmonic oscillator system.
Take, for example, a system as shown in the figure:
$\xi$ denoting the ...
- 31
3
votes
0
answers
62
views
About the various ensembles in Thermodynamics
The properties of a system in thermodynamical equilibrium are described by a partition function:
$$
\mathcal{Z} = \text{Tr} \ e^{-\beta E} = \sum_n e^{-\beta E_n}
$$
This defines so called canonical ...
- 4,724
3
votes
0
answers
65
views
Johnson Nyquist noise with voltage driving
In his 1928 paper, Nyquist derives the famous Johnson-Nyquist noise relation which is, to be very precise according to his paper:
It gives the variance of the voltage at the boundary of a resistor ...
- 1,333
3
votes
0
answers
53
views
Does Heat Equation really describe thermodynamic temperature?
We learnt that in the first PDE course, temperature profile could be described by heat equation.
\begin{align}
\frac{\partial{u}}{\partial t} \;=\; \alpha \nabla^{2}u \tag{1} \label{heat-eqn}
\end{...
- 1,061
3
votes
1
answer
164
views
Is Landau free energy really the free energy?
I recall reading in Negele&Orland's book that Landau free energy function is not really the free energy that one obtains from the partition function $$F = -\frac{1}{\beta}\log Z.$$ Indeed, the ...
- 55k
3
votes
0
answers
40
views
Thermodynamic entropy and energy required for measurement
In the framework of information entropy, one common question is how to develop a code that minimizes the cost of transmission of a message, given that each bit as a fixed unit price. If the ...
- 3,936
3
votes
0
answers
449
views
Statistical definitions of heat and work
My understanding of heat and work from a statistical mechanics perspective (mainly extracted from Schrödinger's Statistical Thermodynamics) is as follows.
We have some system, let us say a box of gas....
- 2,014
3
votes
0
answers
54
views
The first law of Thermodynamic in curved space
As we know, the first law of thermodynamic is $ dE=TdS-PdV+\mu dN $. is it true for a generic metric? what is the covariant form of this equation? for example, I think chemical potential and number ...
- 381
3
votes
0
answers
76
views
Implications of thermodynamic inconsistency in CFD calculations
During my PhD work I had to use tabulated values of thermodynamic properties of gases in some Computational Fluid Dynamics (CFD in short) simulations.
CFD simulations consist in the numerical solution ...
- 57
3
votes
1
answer
379
views
Trick for calculating the thermal entropy of the SYK model in the large $N$ limit
Reading about the SYK model I encounter a trick that should help to calculate the thermal entropy of the system. I am not able to understand what they are doing though. Particularly the part from eq....
- 51
3
votes
0
answers
94
views
Pathria's number of states asymptotic estimation
I'm seeking for a mathematical grounding behind one trick employed in "Statistical Mechanics" book by R. Pathria and P. Beale to calculate the entropy $S(N,V,E)$ of an ideal monoatomic gas by counting ...
- 51
3
votes
0
answers
411
views
2-level system of indistinguishable particles
It is a typical introductory problem in classical statistical physics to calculate the entropy of a two-level-system: say we have a N particle system in which particles can have energy E or 0. ...
- 31
3
votes
0
answers
99
views
Condensed water freezes and other water condenses around it
So I was on a plane and tiny crystals of ice formed on the window glass. This window is formed by a few screens of glass (maybe or maybe not) with vacuum inside. I think the frost was due to some ...
- 1,834
3
votes
0
answers
110
views
Evolution of area during the ring-down of a black-hole merger
My training is in nuclear physics, so my intuition is trained by the liquid drop model, in which the nuclear fluid is incompressible. This leads to the wrong intuition when I try to apply it to the ...
user4552
3
votes
0
answers
60
views
Why do the $C_v$ of gapless systems have a power law behaviour?
The functional dependence of the heat capacity $C_v$ of systems with gapless excitations (e.g., lattice with acoustic phonons, Heisenberg ferromagnet with spin waves etc) is like a power law $$C_v\sim ...
- 25.5k
3
votes
0
answers
90
views
Correlation length amplitudes in Ising 2D model
I am reading the article about Universal amplitude ratios in the 2D Ising model (https://arxiv.org/abs/hep-th/9710019) by G. Delfino.
I have a question about page 3 of the paper. For a magnetic ...
- 439
3
votes
0
answers
43
views
How bad is it if we don't know the distribution of an average?
Let's assume that it takes on average $\langle W\rangle$ work to perform some process.
While we do know that the fluctuations i.e. the difference between single realizations of the process $W_1$,$...
- 395
3
votes
0
answers
195
views
Is there any use of a quadratic equation of state in FLRW cosmology?
Consider standard FLRW cosmology. Usually, the relation between energy density $\rho$ and pressure $p$ of a cosmological fluid component is linear:
\begin{equation}\tag{1}
p = w \, \rho,
\end{...
- 6,858
3
votes
0
answers
96
views
Stress-Strain behavior of ceramics at high temperatures
Can someone explain to me why do we observe the peak in the stress strain behavior at 1400 C and then a sudden decline followed by gradual increase? What does it signify? Does it have anything to do ...
- 31
3
votes
0
answers
88
views
Is it necessary to assume that equivalent microstates cannot get transformed into inequivalent microstates to derive the Landauer principle?
The Landauer erasure principle states that to erase a bit of information from a system, the entropy of the environment will be increased by at least $k_B\log2$, or equivalently, it costs at least an ...
- 9,079
3
votes
0
answers
70
views
From emission probability to black body spectrum. (Hawking radiation as tunnelling.)
In the 1999 paper by Wilczek & Parikh (and in many subsequent papers) the "emission rate" (really the probability of tunneling) of a particle with energy $\omega$ from a static black hole (BH) is ...
- 750
3
votes
0
answers
349
views
Integrated vs. Differential Form of the Enthalpy
I have been under the impression that the definition of enthalpy as
$$H = U + PV$$
is purely mathematical, the result of taking the Legendre transform of the internal energy $U$, and merely provides ...
- 339
3
votes
0
answers
42
views
Are there any black hole information loss solutions that do not resort to non-locality?
It seems as though all solutions to the information paradox resort to non local effects. What solutions do we have that preserve locality?
user164839
3
votes
0
answers
99
views
Statistical mechanics with a freely variable parameter
I would prefer to limit this question to the microcanonical ensemble for ease. I'm particularly interested in the limit that there is no intrinsic cost to introducing particles into a system, in the ...
- 1,352
3
votes
0
answers
63
views
Is Wilson loop particle heavier than black hole in AdS-CFT at finite temp?
Finite temperature is introduced in the Ads Space by inserting a black hole. In the Ads-CFT correspondence, the Wilson loop is at $u \rightarrow \infty$. But the black hole horizon itself would be at $...
- 897
3
votes
1
answer
189
views
Strange units of measurement of heat transfer coefficient in Newton's cooling law
In my finite element software there is the following equation:
in the original Newton's cooling law h has the units $W/(m^2 K)$.
Why here it has the units $W/(m^3 K)$?
- 309
3
votes
0
answers
47
views
Water vapour behaviour during hypersonic expansion
I have a question about the behaviour of air with a small mass fraction of water vapour at extremely low pressures and temperatures.
I am currently running experiments in a large vacuum facility that ...
- 131
3
votes
0
answers
112
views
Quantum Maxwell Demon by Zurek
I just recently started on my bachelor thesis concerning the exorcism of Maxwell's demon. I'm planning to review some of the historical papers in order to capture the demons joyful journey in the ...
3
votes
1
answer
410
views
Wien on Temperature and Entropy
As far as I understand, Wien defines entropy, which he uses in his derivation, as
$$ S = \text{v} \int\limits_0^{\infty} \varphi(\rho, \nu) d \nu, $$
where $\text{v}$ is the volume occupied by ...
- 1,240