Tagged Questions
5
votes
4answers
139 views
Can a single molecule have a temperature?
A show on the weather channel said that as a water molecule ascends in the atmosphere it cools. Does it make sense to talk about the temperature of a single molecule?
3
votes
0answers
36 views
How long would it take for a container in vacuum to leak half of its air?
Let's say I know the size of the container, size of the hole the air leaks through, pressure the air is under and temperature of the air if that helps anything. Is it possible to calculate this only ...
1
vote
1answer
43 views
Sackur-Tetrode equation - clarification required - problem with units
I'm a 2nd year physics undergraduate and recently I've volunteered to give a short presentation on the Sackur-Tetrode equation derivation and its use at removing the Gibbs paradox. I've looked on the ...
2
votes
3answers
81 views
Question about the proof that heat capacity goes to zero if temperature approaches $0K$
I don't completely understand the proof that is given for the claim that the heat capacity goes to zero, if the temperature approaches $0K$.
They do it as follows, if $C_x$ is the heat capacity where ...
3
votes
0answers
46 views
Lattice model completely constrained by boundary data
I am dealing with a lattice model that has the peculiar property that if I specify all the spins on the boundary, by local conservation laws, the whole lattice configuration (throughout the whole ...
4
votes
3answers
179 views
Definition of entropy
In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) entropy of a variable $X$ is ...
1
vote
4answers
85 views
The Preference for Low Energy States
The idea that systems will achieve the lowest energy state they can because they are more "stable" is clear enough. My question is, what causes this tendency? I've researched the question and been ...
1
vote
0answers
32 views
Calculating the change in entropy in a melting process
I have a homework question that I'm completely stumped on and need help solving it.
I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
0
votes
0answers
42 views
Lambda transition data points of $\require{mhchem}\ce{^4He}$
I'm looking to get some data on the lambda transition of $\require{mhchem}\ce{^4He}$. I need the data points of the specific heat vs. temperature graph, if that makes sense.
7
votes
3answers
322 views
Why does the Boltzmann factor $e^{-E/kT}$ seem to imply that lower energies are more likely?
I'm looking for an intuitive understanding of the factor $$e^{-E/kT}$$ so often discussed. If we interpret this as a kind of probability distribution of phase space, so that $$\rho(E) = ...
1
vote
1answer
33 views
How can I find the temperature of this system?
A system was given a small amount of thermal energy dE, and its number of states G grew by 25%. How can I find the system temperature?
The system contains gas particles, I know that $dE << ...
0
votes
0answers
96 views
What is the condition for getting Bose-Einstein condensation? [closed]
Consider an ideal Bose gas in three dimension with energy-momentum relation E proportional to $p^s$ with $s>0$. Find the range of $s$ for which this system may undergo a Bose-Einstein ...
0
votes
1answer
76 views
Uncertainty and Thermodynamics
Dilemma
The uncertainty principle of energy and the 2nd law of thermodynamics don't add up : the uncertainty principle of energy says that
$\Delta \tau \cdot \Delta E \ge \frac{h}{4\pi} = ...
1
vote
1answer
62 views
Maximizing Multiplicity of Einstein Solid == (Temperature = $\infty$)?
If I have a system consisting of 2 Einstein solids (A and B) is it equivalent to say that maximizing the multiplicity of the ...
0
votes
0answers
27 views
Increase in number of micro states explanation or restatement of second law?
Is the boltzmann's expression of entropy as log of micro states leading to the formulation that system is more likely to be in a macrostate with more no. Of micro states really is an explanation or ...
3
votes
0answers
73 views
Spontaneous conversion of heat into work at negative temperatures
Consider a heavy macroscopic object moving in a gas. Friction causes its kinetic energy to be converted into heat. Thermodynamically, there is (effectively) no entropy associated with the kinetic ...
0
votes
1answer
85 views
Math for Thermodynamics Basics
I am studying Statistical Mechanics and Thermodynamics from a book that i am not sure who has written it, because of its cover is not present.
There is a section that i can not understand:
...
4
votes
3answers
320 views
Is there a mechanism for time symmetry breaking?
Excluding Thermodynamic's arrow of time, all mathematical descriptions of time are symmetric. We know the arrow of time is real and we know the equations describing physics are real so is there any ...
4
votes
2answers
147 views
Dispersion relation and Heat Capacity
I have seen case studies of the 3D Debye model where the vibrational modes of a solid is taken to be harmonic with dispersion relation $\omega = c_sk$. It is said that for temperatures much less than ...
0
votes
2answers
140 views
Behaviour of individual terms in Einstein-Smoluchowski fluctuation-dissipation relation
Consider a bath of Brownian particles at temperature $T$. If we sprinkle some larger particles in this (eg: pollen grains in water or dust motes in air), they'll diffuse with diffusion constant $D$ ...
1
vote
0answers
77 views
Rotational Constant and Moment of Inertia of Fluorine gas
I have come across some homework question on thermodynamics which needs me to calculate $B$ of $F_2$
My attempt:
$B= \frac{h}{8\pi^2cI}$ where $I=\mu r^2=\frac{m_1m_2}{m_1+m_2} r^2$
Atomic mass of ...
2
votes
2answers
134 views
Why the temperature is getting lower when the universe is expanding
As we know, if an ideal gas expands in vacuum, as its energy is unchanged, the temperature remains the same. An ideal gas's energy does not depend on volume. In general, the energy is $kT$ times the ...
3
votes
2answers
138 views
Is there a formal definition of a macroscopic variable in statistical mechanics?
Intuitively it's easy to accept that the usual variables like temperature, internal energy, etc. are 'macroscopic', but does there exist a formal definition of a macroscopic variable?
In other ...
2
votes
2answers
241 views
Why is there a Global Minimum for the Morse Potential?
For Diatomic molecules, the Morse potential describes their potential energy as a function of separation distance between the two particles.
My question is, what is the explanation of of the dip ...
2
votes
1answer
63 views
How can dQ/T be interpreted as a system's level of disorder?
Long before statistical mechanics, entropy was introduced as:
$dS = \frac{dQ}{T}$
At the time when entropy was introduced in this manner, was it known that entropy represents how "disordered" a ...
2
votes
1answer
155 views
Maxwell-Boltzmann velocity PDF to CDF [closed]
I asked on Math.SE and was advised to try here instead.
I need to draw from a Maxwell-Boltzmann velocity distribution to initialise a molecular dynamics simulation. I have the PDF but I'm having ...
0
votes
1answer
119 views
relation between first law of thermodynamics and statistical mechanics definition of entropy
From the definition of entropy as $S= - Tr (\rho\, ln \rho)$ one obtains that
$S = \frac{\langle E \rangle}{T} + \log Z.$
The first law of thermodynamics has
$dS = {dE \over T}$.
Why is there no ...
3
votes
1answer
160 views
Why is (von Neumann) entropy maximized for an ensemble in thermal equilibrium?
Consider a quantum system in thermal equilibrium with a heat bath. In determining the density operator of the system, the usual procedure is to maximize the von Neumann entropy subject to the ...
0
votes
1answer
59 views
Indicators on how even the heat is distributed?
I'm wondering if there are any good indicators on how even the heat is distributed on an object (for simplicity, a flat object maybe)? What are the possibly reasonable ways to maximize the evenness if ...
1
vote
1answer
227 views
Constant pressure and temperature mixing of 2 different ideal gases - possible work and heat?
A simple question I hope...
Initially, have two separate containers of 2 different ideal gases, 1.) N1, P, T, V1 and 2.) N2, P, T, V2.
After mixing, the pressure and temperature are still P and T, ...
5
votes
1answer
85 views
Postulate of a-priori probabilities
In Statistical Mechanics, we often postulate that for an isolated system, the phase-space density of all accessible microstates (i.e all microstates consistent with the energy) is the same. This is ...
6
votes
1answer
247 views
Maximum Principle vs. Minimum Principle in Non-equilibrium Thermodynamics
Prigogine's Min. principle states that in steady-state non-equilibrium systems the entropy generation rate is at a minimum, i.e., a system will seek a steady-state that has min entropy generation. ...
1
vote
0answers
38 views
Any new texts directly on second law of thermodynamics? [duplicate]
Possible Duplicate:
Recommendations for Statistical Mechanics book
Is anyone aware of any recent text that summarises the research and arguments on second law of thermodynamics and also on ...
8
votes
3answers
262 views
Could temperature have been defined as $-\partial S/\partial U$?
When coming up with a definition of temperature, it's typical to start with an empirical definition that a system with a hotter temperature tends to lose heat to a system with a colder temperature. ...
1
vote
1answer
84 views
Parameter determining argon phase
Currently I am working a molecular simulation to determine phases of an argon NPT ensemble using Lennard Jones potential. Mainly I use the radial distribution function to determine solid, liquid, or ...
2
votes
1answer
132 views
Phase volume contraction in dissipative systems
I am confused about phase-volume contraction in dissipative systems. Please help me catch the flaw in my understanding. From a macroscopic point of view I understand that a dynamic system tends to go ...
0
votes
1answer
217 views
How much energy Maxwell's demon will earn?
Suppose we have one mole of one-atom ideal gas at temperature $T$.
Suppose Maxwell's daemon has separated molecules into two sections, one with speed below mean and another with speed above mean.
...
1
vote
1answer
112 views
Why can we not reduce the size of a system below the correlation length without qualitatively changing its properties?
This question is posed in the context of thermodynamics/statistical mechanics. Suppose we define the correlation length as the $\xi$ in the exponential factor $e^{-r/\xi}$ that appears in the ...
0
votes
1answer
215 views
Expressions for canonical partition function and probabilities $p(E_i)$
Given an atom with 4 allowed states corresponding to the energy levels
$E_1 = 0$, $E_2 = E$, and $E_3 = 2E$ with degeneracies 1, 1, and 2 respectively.
How do I find the expressions for the ...
4
votes
1answer
129 views
How do I calculate the probability that the oscillator is in a certain state using partition function?
So let's say I have a single ($N=1$) quantum harmonic oscillator and the energy is determined by $E_n = (n + 1/2) \cdot \hbar \omega$ (where $n$ is the quantum number and $n$ = $0, 1, 2, \ldots$)
...
2
votes
1answer
56 views
What does Metric Transitivity Mean?
Jaynes In his paper "Information theory and Statistical mechanics" says
"Previously, one constructed a theory based on equations of motion, supplemented by additional hypothesis of ergodicity, ...
2
votes
1answer
282 views
Physics-based derivation of the formula for entropy [duplicate]
Possible Duplicate:
Proof of $S=-\sum p\ln p$?
I am looking for a derivation of the formula
$$S~=~-\Sigma_ip_i \log (p_i).$$
for entropy, from first principles. I only wish to assume the ...
2
votes
1answer
215 views
What is non-thermal plasma?
I read about non-thermal plasma, but I still have some questions:
The ions and neutral particles are not in thermal equilibrium with the electron, does that mean that the overall temperature is low ...
1
vote
0answers
116 views
An explanation for the Landauer's principle
Has anyone understood the Landauer's principle? What is the current status?
In specific, is there a theoretical derivation of the Landauer's Principle?(not the heuristic one based on Salizard's ...
2
votes
3answers
419 views
Does high entropy means low symmetry?
According to Bogolubov postulate (various texts name it differently) in Non-equilibrium thermodynamics, the number of needed parameters to describe our system is decreasing with time, and finally at ...
4
votes
4answers
212 views
Why can $\beta$ not be linearly proportional to $T$, that is $\beta = constant \times T$?
$\beta$ in statistical mechanics is equal to $\frac{1}{k_BT}$ in in thermodynamics, but I do not understand why $\beta\propto T^{-1}$ instead of, say, $\beta\propto T$?
2
votes
1answer
296 views
Why does the law of increasing entropy, a law arising from statistics of many particles, underpin modern physics?
As far as I interpret it, the law of ever increasing entropy states that "a system will always move towards the most disordered state, never in the other direction".
Now, I understand why it would ...
4
votes
1answer
130 views
Ideal gas and diatomic gas with same temperature
If a box of ideal gas and another box of diatomic gas are in thermal equilibrium,
does it mean that the average translational energy of ideal gas particle (A) is the same as that of diatomic gas ...
5
votes
3answers
380 views
Are negative temperatures typically associated with negative absolute pressures?
Negative temperatures and negative absolute pressures are both possible in physical systems. Negative temperatures arise in (for example) populations of two-state systems, which have a maximum amount ...
1
vote
2answers
220 views
State-dependent diffusions: Fick's law vs. Fokker-Planck's, which and why?
Consider a "state-dependent diffusion": a diffusion process for which the diffusion coefficient $D(x)$ depends on the (stochastic) state $x$ of the system. (An example is provided by the diffusion of ...
