All Questions
Tagged with classical-mechanics thermodynamics
30
questions
96
votes
4
answers
32k
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Physical meaning of Legendre transformation
I would like to know the physical meaning of the Legendre transformation, if there is any? I've used it in thermodynamics and classical mechanics and it seemed only a change of coordinates?
- 1,227
22
votes
3
answers
3k
views
Why exactly do we say $L = L(q, \dot{q})$ and $H = H(q, p)$?
In classical mechanics, we perform a Legendre transform to switch from $L(q, \dot{q})$ to $H(q, p)$. This has always been confusing to me, because we can always write $L$ in terms of $q$ and $p$ by ...
- 103k
3
votes
1
answer
677
views
Collision Term in the Classical Boltzmann Transport Equation
I cannot get over the feeling that in the classical derivation of the collision term of Boltzmann's transport equation molecules that are already knocked out of a $(\textbf r, \textbf v)$ space volume ...
- 31
7
votes
1
answer
612
views
necessary and sufficient conditions for an isolated dynamical system which can approach thermal equilibrium automatically
Given an isolated $N$-particle system with only two body interaction, that is
$$H=\sum_{i=1}^N\frac{\mathbf{p}_i^2}{2m}+\sum_{i<j}V(\mathbf{r}_i-\mathbf{r}_j)$$
In the thermodynamic limit, that ...
- 5,971
6
votes
2
answers
2k
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Symplectic geometry in thermodynamics
There seems to be analogues between Hamiltonian dynamics and thermodynamics given the Legendre transforms between Lagrangian and Hamiltonian functions and all of Maxwell's relations. Poincarè tried to ...
- 2,441
4
votes
2
answers
1k
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Is mean kinetic energy related to temperature of a system of interacting classical particles?
I'm trying to intuitively understand what temperature is for a system of classical particles. The usual definitions via Gibbs measure or entropy appear very unintuitive me. But, as for ideal gas ...
- 29.1k
2
votes
2
answers
775
views
How does the work-energy theorem relate to the first law of thermodynamics?
The work energy theorem states that the net work on a particle is equal to the change in the kinetic energy of the particle:
$$W_{net}=\Delta K $$
My first question is whether this formula (the work-...
- 1,581
11
votes
1
answer
1k
views
7/2 versus 9/2 for diatomic heat capacity
Question
I calculated the classical heat capacity of a diatomic gas as $C_V = (9/2)Nk_B$, however the accepted value is $C_V = (7/2)Nk_B$.
I assumed the classical Hamiltonian of two identical atoms ...
- 2,107
5
votes
2
answers
3k
views
What's the true reason behind thermal expansion?
Thermal expansion is a normal concept everyday. There are 2 explanations:
1, thermal expansion result in stress, then result in deformation
2, thermal expansion result in deformation, then result in ...
- 115
4
votes
6
answers
1k
views
Does work-energy theorem account for thermal energy?
Suppose a box (which I assume to be a rigid body) with an initial velocity that starts to slide on a level surface with friction. Imagine this experiment is done in vacuum, so there is no air drag or ...
- 61
3
votes
4
answers
831
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Why is a temperature gradient set up in a heated rod? [duplicate]
Suppose a cylindrical rod is maintained at 100 degree Celsius and the other at 0 degree Celsius. My book says that after reaching "Steady State" the rod will have developed a constant temperature ...
- 41
3
votes
2
answers
1k
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Is temperature affected by gravitational potential?
Ok, I feel a bit silly asking this. I'm asking in relation to this question here on the molecular basis of hydrostatic pressure in a gas. There's been quite a bit of discussion and one of the ...
- 4,064
1
vote
2
answers
426
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When we push on a wall, can we say work is being done on the atomic particles in contact with our hand?
Since textbooks say work is act transfer of energy, it led me to think of the following assumption:
Work is being done on the the atoms in the wall, in contact with the hands, when we push (hard) ...
- 885
-3
votes
1
answer
234
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Alka Seltzer Model: formulas/models requested [closed]
This evening I became fascinated with how my Alka Seltzer tablet disintegrates over time within a small portion of Diet Lipton Citrus Ice Tea. I used a nearly frozen cup; tall, as one might request in ...
- 15
32
votes
11
answers
5k
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In reverse time, do objects at rest fall upwards?
I want to develop a game where time runs backwards, based on the idea that physical laws are reversible in time. However, when I have objects at rest on the earth, having gravity run backwards would ...
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