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].
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conduction through solids
How is heat transferred through two separate bodies which are in contact. The collision of the lattices of atoms of the two bodies is a good answer but if there is a net energy transfer then shouldn't ...
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Amount of energy to separate Gases - relationship to concentration
I want to understand the efficiencies of separating mixed gases, and for that I want to understand the thermodynamic limit case. Looking at the wikipedia page for entropy of mixing, I find the ...
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Why do system tend to attain thermal equilibrium anyway?
Ok, so I was reading a chapter on thermodynamics (introduction), which built its content on the idea that two systems separated by a diathermic wall will tend to attain thermal equilibrium with each ...
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Can the temperature gradient between an aircon's hot output and air outside do work and save part of aircon energy?
I usually see air conditioners releasing hot air from the inside to the world outside. But since it is warmer than the air outside, I cannot see why this gradient could not do some work and possibly ...
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A question regarding Open, Closed and Isolated systems
While revising Chemical Thermodynamics as usual, I came across a term called Closed System - which is defined as a system which exchanges energy with the surroundings and not matter. But, according ...
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How to modify kinetic gas theory to work for macroscopic particles? (2D)
For the first time I framed a question on my own when I was recently playing carrom pool with my cousin and a striking thought ran across my mind!
I was thinking if a square frame is fixed rigidly on ...
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Hawking Temperature for a hairy BTZ Black Hole
The metric of a hairy Black Hole is given by:
$$ds^2 = \frac{L^2}{z^2}\biggl(-g(z) dt^2 + \frac{e^{2 A(z)}}{g(z)} dz^2 +d\varphi^2\biggr), $$
where $L$ is the AdS length taken to be $1$,$A(z)$ is the ...
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Interior Hawking radiation
The Hawking effect is induced by the causal horizon of a black hole, which separates the interior and exterior modes such that asymptotic observers at infinity see thermal radiation flux. What can we ...
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BTZ partition function
I am unable to obtain the internal energy of the BTZ black hole. Recall its metric, which is given by
\begin{align}
ds^2=-N^2(r)dt^2+\frac{dr^2}{N^2(r)}+r^2\left(d\phi+N^\phi(r)dt\right)^2\,,
\end{...
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Beyond the energy equipartition, what is the uneven law?
There is a celebrated energy equipartition theorem, it works fine for many systems. But it requires the dense filling of the surface of constant energy. What if there are other conserved quantities, ...
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How does Viscosity of the Sun varies as we go from core to the convective zone?
How does Viscosity of the Sun varies with its radius?
For. eg, Here is the graph of the Density of the sun v/s radius. I am looking for the Viscosity v/s radius plot.
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The replica trick
Assume that I have an interaction term of the form
$$\sum_{i=1}^{N}\sum_{a=1}^{M}g_i f_{i,a}^{\dagger}f_{i,a}\sigma_z $$
where the $g$'s are random and taken from the gaussian ensemble and
$f_{i,a}$ ...
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Statistical mechanics with multiple species
How do we derive the equivalent of the Boltzmann distribution when there are multiple species in equilibrium?
I'm thinking of situations where there are multiple species of particle involved, and they ...
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In kinetic theory of gases, in finding connection between pressure and molecular kin. energy, why $N/2$ & not $N/6$ molecules are assumed to hit wall?
In my book While driving a relation between pressure and average kinetic energy of a single molecule [i.e. $P = (Nmv^2)/2$ ], an ideal gas of $N$ molecules is assumed to be enclosed in a cubical box ...
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Conservation of Extensive Quantities
Thermodynamic quantities are usually divided into two categories: extensive and intensive. The extensive category is sometimes modified to be an extensive density measured relative to unit mass or ...
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What's wrong with this thermodynamics argument on the cosmological constant?
I'm puzzled by the following thermodynamics argument on the cosmological constant interpreted as a perfect fluid of pressure $p = -\, \rho$. I start considering a simple fluid of local energy density ...
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How can I remove a layer of Silica from a rough IN718 surface?
Our rocketry group is designing a biliquid ethaLox Inconel 718 additively manufactured chamber.
We are looking into using Tetraethyl orthosilicate as a fuel additive to reduce the heat flux in our ...
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How often does a molecular machine run in reverse?
I was reading the Wikipedia article on Stochastic thermodynamics, and came across this statement in the overview:
When a microscopic machine (e.g. a MEM) performs useful work it generates heat and ...
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Thermodynamics Chain Rule And Independent Variables
I was reading my textbook and I came up across the entropy $S(T,V,N)$ where temperature $T$, volume $V$, and number of particles $N$ are the independent variables. According to the chain rule the ...
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How to avoid the Cosmological Horizon problem in the Tethered Galaxies problem?
I found an interesting article by Edward Harrison [1] who proposed a way to harness energy from spacetime expansion by attaching a string to a receding cosmic object (like a galaxy). However, one ...
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Maxwell distribution solely using the Stosszahlansatz and geometric transformations?
Background
To quote Wikipedia:
The assumption of molecular chaos is the key ingredient that allows
proceeding from the BBGKY hierarchy to Boltzmann's equation, by
reducing the 2-particle distribution ...
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Variation of Relative Humidity (RH) in closed room vs outside
I have an insulated garage room with the doors closed, and I am interested to monitor the Temperature + Relative Humidity (RH) inside the room, compared with outside. I have taken some readings ...
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Why is the low entropy state of the infant universe problematic?
According to the second law of thermodynamics, the entropy of a closed system increases (or in energy terms, the Gibbs free energy decreases, or in temperature language, the temperature tends to the ...
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Deriving Hawking temperature "from" Unruh effect and their relation
Let me recall some basic computational facts (the meaning of which I am trying to understand).
In flat space, an adapted coordinate $(\tau, \xi)$ associated with an observer with constant proper ...
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Understanding thermal wavelength and de Broglie thermal wavelength
One of the areas in which the concept of de Broglie wavelength is important has to do with the fact that if the interparticle distance of a 3D gas is larger than the thermal de Broglie wavelength then ...
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How does the heat energy from burning a gallon of gasoline compare to the solar energy the resulting $\rm CO_2$ absorbs in the atmosphere?
I think essentially all of the energy from a gallon of gasoline burned in, say, a car is eventually converted into heat in the atmosphere. But I don't think the heat from burning fossil fuels ...
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What does Specific Heat capacity of a material depend upon?
I have read in many places that specific heat capacity is an property of the material but I haven't really understood what it depends upon, as in what factors affect that specific heat, I have thought ...
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What exactly is the specific heat of a gas?
When I read that specific heat of Steam $(100 °C)$ is $2010 J/kg \cdot °C$ what exactly am I reading?
What does specific heat of a gas essentially mean when it is not mentioned whether it was measured ...
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Kinetic-molecular model of an ideal gas, speed
We make the statement that $v^2 = v_x^2 + v_y^2 + v_z^2$ where $v$ is the speed of the particle.
This is equivalent to saying $v^2 = 3*v_x^2$.
But then we supposedly encounter the problem that when ...
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Peak of energy and black body
The tungsten filament of an incandescent light bulb has a temperature of approximately 3000 K. The emissivity of tungsten is approximately
1/3, and you may assume that it is independent of wavelength. ...
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Why does water collect under a book my laptop is sitting on?
Sometimes I sit in my bed with a blanket over my lap. On top of the blanket I put a hardcover book. On top of the book I will be working on my laptop. So we've got:
Laptop
Book
Blanket
My lap
...
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Geometric Entropy & the Partition Function for Conical Deficits
In their paper, Callan and Wilczek claim to derive from the thermal entropy
$$S_\text{thermal} = -\left(\beta\frac{\partial}{\partial\beta}-1\right)\ln(\mathcal{Z})$$
a geometric entropy which is ...
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Negative surface tension of de Sitter event horizon?
Questions –
What does a negative surface tension of a de Sitter cosmological event horizon actually mean? Scotch in water, or something else?
What does a zero ‘external’ vacuum pressure to the de ...
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How much does the temperature increase after the saturation of the material due to the magnetocaloric effect?
If we assume a point in the M-H curve of matter that is the complete saturation of matter, from this point onwards (with increase in magnetic field), do we have an increase in temperature in relation ...
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General Method for Calculating Excluded Volume
In section 5.3 of Kardar's Statistical Physics of Particles, the van der Waals equation is given as:
$[P+\frac{u_0 \Omega}{2}(\frac{N}{V})^2][V-\frac{N\Omega}{2}]=Nk_BT$
The van der Waals parameters ...
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Why cant there be a sonic velocity inside the convergent part of a nozzle? (ie upstream of the throat)
A convergent-divergent nozzle is typically used for accelerating or decelerating airflow to or from supersonic speeds. The typical configuration for such a nozzle is the de Laval nozzle that is ...
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How can you determine how fast (m/s) heat will travel through a material being heated on one end?
I was wondering how fast heat will travel through rectangular glass bottle, heated on a tray under vacuum.
I work in a lab where an inert atmosphere glovebox is used, and when moving glass bottles ...
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How is entropy defined for a quantum field?
I know that in nonrelativistic quantum mechanics the entropy of a mixed state $\rho$ is defined as
$$S=-k_B~\mathrm{tr}[\rho~\mathrm{ln}\rho].$$
But what about quantum field theory, or even just ...
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Proving that the CMBR remains thermal after a Lorentz boost
Suppose $S$ is a frame in which the CMBR is thermal and isotropic. I'm taking this to mean it follows the Planck Blackbody distribution $$n(\omega)=\frac{1}{\pi^2 c^3}\frac{\omega^2}{e^{\beta\hbar\...
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In which cases you use free energy to calculate pressure?
From thermodynamic identity you get:
$$\left(\frac{\partial U}{\partial V}\right)_{S,N} = -P$$
But with Helmholtz free energy $F = U-TS$, we can also get pressure from this equation:
$$\left(\frac{\...
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Interpretation of probability in Statistical Mechanics
In statistical mechanics, in particular the canonical ensemble, the probability of the system to have a particular state is given by : $$P_i=\frac{e^{-\beta E}}{Z}$$
Here $Z$ is the partition function ...
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How to express pressure variance in the canonical ensemble of statistical mechanics?
The variance of pressure can be written as $<p^2> - <p>^2$. What is another way to express this? I found $\left<(p-<p>)^2\right>=\frac{k_B T^2}{C_v}\left(\frac{\partial P}{\...
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Can one derive Planck's law by considering a more "natural" setting?
I have been wondering about this for a while. I've recently become a bit dubious regarding the usual derivation cited in textbooks of Planck's law (and its inaccurate predecessor, the Rayleigh-Jeans ...
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Oil pooling along grates in heating pan
Recently I went to cook something on my cast iron pan. I turned the burner on, drizzled in some oil (I think it was olive oil) and started chopping some vegetables. When I turned back a few moments ...
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Are quantum dot’s immobile?
In a recently closed question regarding the cooling of quantum dots through lasers has one of the commentators state that this is in fact impossible as QD’s are immobile:
Can quantum dots temperature ...
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Can a pool of water be used to reflect heat from light?
I am designing a low impact house. I had planned to use a reflecting pool of water to increase the passive solar gain in the house in winter:
and reflect it away in the summer (note the structure on ...
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Is the entropy of a black hole relative?
I have a question about the entropy of black holes. Well, some time ago I was able to demonstrate theoretically that the entropy of black holes should be relative, that is, depend on the observer.
But ...
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"Pointlike" explosions: the transition to non-explosions as initial energy is decreased (or volume increased). How does their behaviour change?
If a large enough amount of energy is dumped in a small enough volume of Earth's lower atmosphere, events follow a standard pattern:
The air within the volume is fully ionized and heated to extremely ...
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Understanding the critical temperature on a $pV$ diagram
I know that the critical temperature is the highest possible temperature before a liquid becomes a gas. I also know that at the critical volume on the critical temperature isotherm, $\frac{\partial P}{...
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Why does the divergenceful part of the electric field not produce an ultraviolet catastrophe?
In this answer to a question about how to show the electromagnetic field has particle excitations (photons) it shows that the divergenceful part of the electric field doesn't have a field that it is ...
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