All Questions
44
questions
0
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1
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48
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Why the interaction between system and thermal bath does not affect the energy levels of the system?
When we write down the full Hamiltonian of a system in contact with a thermal bath, it is as follows:
$$H_{\text{total}} = H_{\text{system}} + H_{\text{system+bath}} + H_{\text{bath}}.$$
As our focus ...
- 1,068
2
votes
0
answers
79
views
What is the connection between energy in classical mechanics and thermodynamics
In classical mechanics the concept of energy is very simple. If I have a bunch of particles $r_1$...$r_n$. Then the total energy is:
$$E=\frac{1}{2}m(\dot r_1^2+...\dot r_n^2)+U(r_1...r_n)$$
Now in ...
- 29
5
votes
0
answers
80
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In statistical mechanics, why is one "allowed" to treat classical systems probabilistically?
Is the essential argument that these systems are microscopically chaotic enough that we can approximate their evolution as random (vastly simplifying calculations) and still make accurate experimental ...
- 161
1
vote
1
answer
129
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Standard deviation of kinetic energy approaches average kinetic energy
I have a simulated system of lots of particles modeled as circles moving in 2 dimensions. They bounce off each other and off of walls. Momentum and kinetic energy are conserved.
I noticed that the ...
- 41
-1
votes
2
answers
487
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What are some examples of microscopic quantities?
Mass, volume, energy, entropy, temperature, pressure are some macroscopic quantities. Which means we can think of them even without considering the molecular nature of matter.
What are some examples ...
- 521
1
vote
0
answers
85
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Equipartition theorem for continous medium
The equipartition theorem states that if $x_i$ is a canonical variable (either position or momentum), then
$$\left\langle x_i \frac{\partial \mathcal{H}}{\partial x_j}\right\rangle = \delta_{ij}\ k T.$...
- 133
0
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1
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40
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Expected energy in micro-canonical and canonical distribution
Which relation $E(β)$ is required to ensure that he micro-canonical distribution and the canonical
distribution have the same expected energy?
- 23
1
vote
0
answers
60
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Does the Legendre transformation describe two views on the same physical system or different physical systems?
In mechanics we perform the Legendre transform to go from the Lagrangian $L(q, \dot{q})$ to the Hamiltonian $H(q, p)$. This seems to be describing the same physical system. $L$ and $H$ both describe ...
- 131
3
votes
2
answers
1k
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Very briefly, what is the relation/difference between classical field theory and classical thermodynamics/statistical mechanics?
This is probably not a good question, since I am at a fairly low level, but I am a little bit confused when the two concepts were described to me and it's bringing discomfort during my study.
What I ...
- 243
4
votes
0
answers
63
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How negligible is a term in the internal energy for the equipartion theorem in classical mechanics?
The equipartition theorem is a well-known result of classical statistical mechanics, and it states that if the Hamiltonian of a system can be written like this:
$$H=\sum_{j=1}^m {\alpha_j\ {x_j}^2}$$
...
- 41
1
vote
2
answers
304
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Why should layers of air rise up and the layer above it takes it place
I am a high school student and I am very confused in a topic dealing with "why hot air rises up" I know it is already answered but the answers are difficult for me to understand I want a ...
0
votes
0
answers
42
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Details on why temperature is lower at high altitude
I have read at so many places that warmer air moves up as hotter substances expands and as it rises it loses its kinetic energy and it gets converted into its potential energy(gravitational+...
0
votes
1
answer
115
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Deduction of the entropy balance equation with input and output of matter by convection (mass flow)
In many books of Engineering thermodynamics, the entropy balance equation is wrritten as
$\frac{dS}{dt}=\Pi_S+I_S$
$I_S=\sum_{j=1}\frac{\dot{Q}_{j}}{T_j}+\sum_{i=1}\dot{m}_is_i-\sum_{e=1}\dot{m}_es_e$
...
- 3
9
votes
2
answers
1k
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Does quantum mechanics halve the dimension of phase space?
In classical mechanics, a particle confined to move along only the $x$-direction can be fully described by a 2-tuple $(x_1,p_1)$ in phase space. In this case, the phase-space is clearly 2-dimensional. ...
- 1,581
1
vote
1
answer
105
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Why is it said that entropy of a closed system may increase in classical physics?
Why is it said that entropy of a closed system may increase in classical physics?
A classic thought experiment to explain this claim is that of a closed box with some moving billiard balls initially ...
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