All Questions
Tagged with classical-mechanics thermodynamics
193
questions
96
votes
4
answers
32k
views
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
32
votes
11
answers
5k
views
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 ...
- 422
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
18
votes
1
answer
3k
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Mechanics + Thermodynamics: Bouncing Ball
In preparation for an exam, I'm revisiting old exam questions. This one seems neat, but also quite complicated:
A soccer ball with Radius $R=11cm$ is inflated at a pressure of $P =9 \times 10^4 Pa$,...
- 14.9k
12
votes
3
answers
9k
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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 ...
- 20.4k
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
9
votes
2
answers
1k
views
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
9
votes
2
answers
2k
views
Free energy of coupled classical harmonic oscillators
I'm looking to find the thermodynamic (NVT) free energy of a classical coupled harmonic oscillator system such as the one below:
(image taken from http://openmetric.org/StatisticalPhysics/equilibrium/...
- 949
8
votes
4
answers
12k
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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 ...
- 9,910
8
votes
1
answer
828
views
Entropy and classical mechanics
I was trying to understand what entropy means in the context of classical mechanics, but unfortunately I'm now more confused than I started. Reading, for example, the Wikipedia article on the Second ...
- 661
8
votes
1
answer
225
views
Are Carnot engine efficieny and Fourier heat trasmission law related?
It just occured to me that the efficiency of Carnot cycles is $\eta= \frac{T_1 - T_2}{T_1}$, that is, the efficiency decreases as the difference between reservoir temperatures decreases. On the other ...
- 590
7
votes
2
answers
2k
views
Why does thermodynamic integration work?
Brief introduction:
Thermodynamic integration is a neat computational method used mainly for computing free energy differences between target and reference states of classical many-body systems, such ...
- 4,685
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
7
votes
2
answers
606
views
Liquid column "recoils" in a sealed cylinder when hit by a piston -- is it possible?
Consider a cylinder filled partially with a liquid (e.g. water). The cylinder is sealed, and is at held at room temperature (e.g 298K). At equilibrium (or when no external disturbance is imparted to ...
- 211
7
votes
2
answers
714
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Why doesn't a Brownian ratchet provide free energy?
A Brownian ratchet is described here at Wikipedia.
The "why it fails" section reads:
Feynman demonstrated that if the entire device is at the same temperature, the ratchet will not rotate ...
- 343