Questions tagged [adiabatic]
Thermodynamic processes that occur without exchanging heat between the system and its environment.
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If the ground states of interacting QFTs are so complicated, how did Nature find them?
My question was inspired by trying to understand the paper Quantum Algorithms for Quantum Field Theories, by Jordan, Lee, and Preskill. The main result of that paper is that scattering experiments in ...
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The notion of an adiabatic process in thermodynamics -vs- quantum mechanics
I'm confused about the terminology in the two contexts since I can't figure out if they have a similar motivation. Afaik, the definitions state that quantum processes should be very slow to be called ...
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How slow is a reversible adiabatic expansion of an ideal gas?
A truly reversible thermodynamic process needs to be infinitesimally displaced from equilibrium at all times and therefore takes infinite time to complete. However, if I execute the process slowly, I ...
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Why are sound waves adiabatic?
I want to know why we can treat sound waves as an adiabatic process. Precisely, I know that pressure and density vibrations occur so fast that molecules have no time to exchange energy (I might be ...
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Principle of Caratheodory and The Second Law of Thermodynamics
Background
Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be ...
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Formula for molar specific heat capacity in polytropic process
I found this formula for a polytropic process, defined by $PV^n = {\rm constant}$, in a book:
$$C = \frac R{\gamma-1} + \frac R{1-n} $$
where $C$ is molar specific heat and $\gamma$ is adiabatic ...
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How is this process not quasi-static yet reversible?
Consider a (adiabatic) canister with a piston containing some gas kept in a vacuum. There are two weights on the canister which equalize the pressure of the gas on the piston. Assume the system is at ...
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Adiabatic theorem and Berry phase
As far as I can check, the adiabatic theorem in quantum mechanics can be proven exactly when there is no crossing between (pseudo-)time-evolved energy levels. To be a little bit more explicit, one ...
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Adiabatic piston: why is Callen's argument flawed?
This question is related to this one. I would ask you to read that question and my answer to the question itself before answering this one.
The problem is the following. In his book Thermodynamics, ...
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When is the adiabatic approximation for solid state systems valid?
The adiabatic approximation for solid state systems is rather radical. I was wondering in which cases it breaks down.
As it is based on the idea of the nuclii being much heavier than the electrons I ...
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Basic Thermodynamics: Quasistatic Adiabatic Process
I'm going through the exercises in a Thermodynamics book, just to revise and build my intuition. Right now, I'm working on:
Show that for a quasistatic adiabatic process in a perfect gas, with
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How is ideal gas law applicable to real gas?
I read one of the questions here on physics.stack exchange proving how the speed of sound increases with temperature using ideal gas law equation and adiabatic index. Here's the link:
How can the ...
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How to understand the indeterminate process in thermodynamics?
Consider a closed composite system with an internal movable adiabatic wall. If we release the piston, thermodynamics cannot determine the final equilibrium state (the temperature cannot be determined)....
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Why does a gas get hot when suddenly compressed? What is happening at the molecular level?
My guess is that the molecules of gas all have the same speed as before, but now there are much more collisions per unit area onto the thermometer, thus making the thermometer read a higher ...
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Entropy change in the free expansion of a gas
Consider the adiabatic free expansion of a gas since there is no external Pressure hence Work done on the system is 0 and since the walls are insulated (hence adiabatic) the heat absorbed is 0. ...
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Is there a generalization of the adiabatic theorem into a degenerate Hamiltonian?
Adiabatic theorem states that if the Hamiltonian of the system $H(t)$ is slowly changed, and if the initial state is in the $n$th eigenstate of $H(0)$, then the final state will remain in the $n$th ...
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Why is adiabatic process isentropic?
I have read that adiabatic process is isentropic because there is no heat exchange in an adiabatic process and thus no change in entropy.
But my question is - Even in adiabatic process, work can be ...
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Adiabatic invariant and Liouville's theorem
It appears that many people have tried to show adiabatic theorem from Liouville's theorem, e.g., Li's note, or at least tried to find some relations, e.g., Rugh, Adib and Tong's lecture notes Sec. 4.6....
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Are reversible adiabatic processes always isentropic?
If my understanding is correct, neither reversible nor adiabatic processes are necessarily isentropic.
But are reversible adiabatic processes always isentropic?
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Adiabatic Quantum Computing: why not just set the system in its problem Hamiltonian $H_{P}$ immediately?
Background: In any adiabatic quantum computer (AQC) algorithm, we solve problems in the following manner: We have an initial Hamiltonian, $H_{0}$, whose ground state is easy to find, and a problem ...
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Adiabatic Process: Fast or Slow? [duplicate]
I have always used adiabatic process to be fast, so that the system doesn't get enough time to exchange energy in the form of heat. But as I was reviewing adiabatic process from the Resnick, Halliday, ...
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Adiabatic expansion in van der Waals gas [closed]
Given a Van der Waals gas with state equation:
$$\left( P+\frac{N^2 a}{V^2}\right)\left( V-Nb \right)=NkT,$$
show that the equation of an adiabatic process is:
$$\left( V-Nb\right)T^{C_V}=\text{...
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Adiabatic expansion in the atmosphere
When an air parcel rises and cools adiabatically, it is said that there is no heat transfer as work is done on the surrounding atmosphere as the parcel expands. The parcel loses internal energy and ...
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How does adiabatic cooling make a nebula colder than the CMB?
According to measurements, the gas from the Boomerang Nebula is expanding so fast that it's colder than the cosmic microwave background radiation... how does such a simple mechanic work on such a ...
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Importance of energy relation in Landau & Lifschitz "Statistical Physics"?
At the end of section 11 in "Statistical Physics" by Landau & Lifschitz, a supposedly important equation is derived.
...
Comparing (11.1) with (11.2) we find:
$$\frac{\overline{\partial ...
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A question about the energy of turning on and off interaction adiabatically in QFT
I read a saying as follows:
In a theory with no particles which decay and no bound states, the turning on and off of the interactions merely serves to limit the effective range of forces. In this ...
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What is the Laughlin argument?
The fundamental question is
Why is Hall conductance quantized?
Let's start with the Hall bar, a 2D metal bar subject to a strong perpendicular magnetic field $B_0$. Let current $I$ flow in the x-...
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Why isn't the free expansion of a gas in an adiabatic container isentropic?
If you expand a gas adiabatically using a piston, the process is isentropic. However, if you simply remove the piston and let the gas expand freely, the process is now not isentropic. What makes these ...
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Why the entropy change is not zero in the irreversible adiabatic process?
Why the entropy change is not zero in the irreversible adiabatic process?
...while it is defined as the integral of the heat added to the system over its temperature.
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What is the difference between reversible and irreversible adiabatic expansion?
What is the difference between reversible and irreversible adiabatic expansion?
Is it true that the work done by the gas is the same but the pressure applied externally differ between two process?
If $...
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Isentropic processes
I'm having trouble understanding why reversible adiabatic processes are isentropic.
I understand that in a reversible adiabatic process there is no heat exchange and so $dQ = TdS = 0.$ However, if ...
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Rigorous Laughlin pumping argument
Is there a way to justify formally the Laughlin pumping argument? It is often argued that the spectral flow of Landau levels while varying the flux inserted through the Corbino ring should account for ...
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Can we apply $pV^\gamma$=const only for quasistatic adiabatic process?
But If this is so, I have often seen people applying this formula for quick processes where no heat exchange is possible.
Here is an example from where I am quoting the following:
we will assume ...
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Adiabatic proccess and Carnot cycle in a photon gas
I am making a comparation between the photon gas and the ideal classic gas for my Thermodynamics class. The photon gas is defined by the equations:
$$U=aVT^4 $$
$$P=\dfrac{1}{3}aT^4$$
I found this ...
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Adiabatic fluctuations
In Baumann's cosmology lecture, chapter 4, page 89, he defines adiabatic perturbation as:
Adiabatic perturbations have the property that the local state of matter (determined, for example, by the ...
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Adiabatic theorem - quantum mechanics and thermodynamics [duplicate]
A diabatic process is defined as follows:
Rapidly changing conditions prevent the system from adapting its configuration during the process, hence the spatial probability density remains unchanged. ...
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Instantaneous eigenstate and time dependent Schrodinger equation
Instantaneous eigenstate $\psi(t)$ is defined as
$\hat H(t)\psi(t)=E(t)\psi(t)\tag{1}$
But in the lecture notes of Quantum Physics III MIT (in the section of adiabatic approximation), it is written ...
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How to understand the quantum adiabatic theorem intuitively?
The quantum adiabatic theorem states that: A parametric system remains in its instantaneous eigenstate (with a phase difference) if one of the parameters of the Hamiltonian changes slow enough. This ...
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Where does the heat come from when rubber is stretched adiabatically?
As I understand when a rubber band is stretched adiabatically (which I am assuming means no change in entropy and so no heat flow from surroundings) its polymers naturally are straightened and thus ...
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Condition for adiabatic approximation, derivation?
In quantum mechanics it is said that an adiabatic approximation is valid when
$$T\gg \frac{\hbar}{\Delta E},$$
where $T$ is the time scale of variation of the Hamiltonian and $\Delta E$ is the typical ...
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Schrodinger basis kets with Time-dependent Hamiltonian
I was reading through the proof of the Adiabatic Theorem (in Sakurai) and I realised I'm not quite sure how Schrodinger Basis kets behave when we have a time-dependent Hamiltonian. I know that with a ...
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Are stationary quantum states attractors?
While explaining the quantum adiabatic theorem recently, I appealed to a thermodynamic analogy: when slowly contracting the walls containing a classical gas, the relaxation timescale can be taken to ...
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Temperature change in a gas tank on a car [closed]
There is a beautiful question I ran into:
A gas tank filled with gas at temperature $T$. The gas is at rest first. It is accelerated to a constant velocity of $V$. Assume the process is adiabatic.
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Comparison between isobaric, isothermal and adiabatic expansion
Please check if my understandings of these terms are right because they are a bit confusing to me.
For all three types of expansions, a change in volume means work is done by the system to the ...
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Adiabatic Invariant when forcing is at the natural frequency of a classical simple harmonic oscillator
Consider a simple harmonic oscillator of unit mass, natural frequency $\omega_0$, given by the Hamiltonian
\begin{align}
H_0(q,p)=\frac{1}{2} \left[ p^2 + \omega_0^2 q^2 \right] \ .
\end{align}
Now ...
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Is reversible adiabatic process possible?
Is it possible to have reversible adiabatic process in practical?
because if it is a reversible process than we allowing it to exchange heat with surroundings. If it is in insulation than either we ...
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Thermo homework (HW) problem
I do not believe this question can be solved with the thermodynamics knowledge that I have learned thus far, but someone correct me if I am wrong:
A 0.2-m³ tank containing helium at 15 bar and 22°C ...
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Transitionless quantum driving for specific eigenstates
Transitionless quantum driving is a concept that was invented by Berry in 2009.
In his article on transitionless quantum driving he showed that it is possible to speed up adiabatic evolution of ...
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Why is the value of the heat capacity ratio $\gamma$ never less than 1?
For an monoatomic gas, the value of the heat capacity ratio $\gamma$ is 1.67
For diatomic gases, the value of γ (gamma) is 1.40
For many atomic gases, the value of γ (gamma) is 1.33
It's never less ...
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Adiabatic reversible and irreversible process
If I have 2 gases $A$ and $B$ which are at an initial state ($P_1$,$V_1$,$T_1$), and one gas say $A$ is taken through a reversible adiabatic process and the other gas $B$ through an irreversible ...
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