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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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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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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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( ...
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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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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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547 views

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 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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331 views

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 ...
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366 views

Adiabatic approximation

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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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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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 ...
5
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243 views

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 ...
5
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610 views

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 ...
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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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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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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 ...
4
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166 views

Are energies non-transferable in the Born-Oppenheimer approximation, and when does it apply?

Adiabatic approximation or the Born-Oppenheimer approximation is used whenever the electronic motion is too fast that the electrons effectively see static nuclei and the nuclei, in turn, see an ...
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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 ...
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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. ...
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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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Eigenvalue of the adiabatic Hamiltonian of Farhi's three qubit 2-SAT problem

I was trying to reproduce example 3.3 of Quantum Computation by Adiabatic Evolution by Edward Farhi et. al. This is an adiabatic algorithm to solve an instance of three qubits 2-SAT problem. I think ...
3
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1answer
123 views

Dry adiabatic lifting

If an unsaturated air parcel ascends adiabatically in the atmosphere with an initial temperature, would the final temperature of the air parcel, when it reaches it's destination, be the same at the ...
3
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How do you explain the fact that when air expands freely into an evacuated chamber from a constant pressure atmosphere, its temperature increases?

I came across this paper: Baker, B. (1999). An easy to perform but often counterintuitive demonstration of gas expansion. American Journal of Physics, 67(8), 712-713. ...
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Intuition behind Hamiltonian

I am reading this paper by Das et al. which converts Deutsch's algorithm into an adiabatic quantum algorithm. I don't get the intuition behind the initial and final Hamiltonians. If defines the ...
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70 views

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 ...
3
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1answer
248 views

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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Adiabatically stretching a rubber band

When a rubber band is stretched it heats up, but how can this be explained (from the microscopic view) in the case of an adiabatic expansion (meaning that the entropy remains constant). Further more ...
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Thermodynamics of expanding nitrogen bubble as it rises in water

Problem An air bubble is released from a nitrogen tank 20 meters under water. The bubble has a radius of 1 mm. What will be the radius of the bubble when it reaches the surface? My Questions Is it ...
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572 views

What defines the adiabatic flame temperature?

What defines the adiabatic flame temperature? In a case I have to solve, I need to describe the combustion of natural gas (Groningen natural gas, to be specific). However, I am having some problems ...
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Different forms of the Adiabatic Theorem

I've been reading several papers on Adiabatic Quantum Computation, and I am confused by the form in which the adiabatic approximation condition is presented. For example (quant-ph/0001106 eq 2.8) ...
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How is the energy/eigenvalue gap plot drawn for adiabatic quantum computation?

I was going through arXiv:quant-ph/0001106v1, the first paper by Farhi on adiabatic quantum computation. Equation 2.24 says, $$\tilde{H}(s) = (1-s)H_B + sH_P$$ which means the adiabatic evolution ...
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2answers
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Adiabatic process of an ideal gas derivation

I am working through the derivation of an adiabatic process of an ideal gas $pV^{\gamma}$ and I can't see how to go from one step to the next. Here is my derivation so far which I understand: ...
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1answer
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Sources to learn about Berry phases and Adiabatic Theorem

I recently went through Griffiths' Quantum Mechanics text and there is a chapter called the Adiabatic Theorem that includes Berry phase and the Aharonov-Bohm effect. As I found them very ...
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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? ...
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Is it Possible to have Adiabatic Processes other than $PV^\gamma$ for the ideal Gas?

Is it possible to represent an adiabatic process for an ideal gas by a formula other than $PV^\gamma=Const$?: Relevant Considerations: We always need to connect a pair of arbitrary points/states ...
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1answer
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Proof of adiabatic theorem on Wikipedia

I'm having trouble following the proof of the adiabatic theorem (apparently due to Messiah) on Wikipedia. At one stage we have: $U(t_1,t_0)=1+{1\over i}\int_{t_0}^{t_1}H(t)dt+{1\over ...
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1answer
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Bernoulli Equation for isentropic ideal gas flow

If one derives the Bernoulli Equation for the isentropic ideal gas flow you get: $$ \frac{1}{2}v^2 + g z + \left(\frac{\kappa}{\kappa -1} \right) \frac{p}{\rho} = const. $$ Two questions: Is ...
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Infinite quantum well width $L$ to $2L$ adiabatic process

If we change width of the infinite quantum well $L$ to $2L$ slowly enough, how it does change energy levels.
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Simplest Live Demonstration of Adiabatic Transport

I have to give a presentation on Berry phase. I would like to give the simplest live demonstration of adiabatic transport. If I move an object in a loop and return that object back into its original ...
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Ordering of eigenstates in the quantum adiabatic theorem

Suppose we have an 'initial' Hamiltonian $H_{i}$ whose eigenvalues are all non-degenerate, which we order as follows: $ E^{0}_{i} < E^{1}_{i} < \dots < E^{N-2}_{i} < E^{N-1}_{i}$ Suppose ...
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1answer
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What is the criterion for a change to be adiabatic?

I'm trying to understand whether the change of a parameter $\lambda$ of a Hamiltonian $H$ is adiabatic. Reading Landau and Lifshitz "Mechanics", I see ... let us suppose that $\lambda$ varies ...
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Steady-state adiabatic nozzle, unknown exit velocity & temperature [closed]

The question is 2.10 taken from: Introductory Chemical Engineering Thermodynamics, 2E by Elliot,Lira Air at 30ºC and 2MPa flows ata steady state in a horizontal pipeline with a velocity of 25m/s. ...
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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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Adiabatic theorem in the regime of quantum optics

I am wondering whether there is a version of adiabatic theorem in the regime of quantum optics. My understanding of quantum optics involves with the interaction between photon and atom. This ...
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Adiabatic filling of a container

Suppose a thermally insulated container is filled with atmospheric air until the pressure reaches 5000 psi. This could represent the filling of a diving cylinder, before thermal dissipation becomes ...
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Change in entropy of two isolated systems merged into one system

From Statistical Physics, 2nd Edition by F. Mandl: Two vessels contain the same number $N$ molecules of the same perfect gas. Initially the two vessels are isolated from each other, the gases ...
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How can a reversible adiabatic expansion not increase entropy?

In the second stage of the Carnot cycle, a gas is thermally insulated and allowed to expand and do work on the piston. I understand the reason people give is that because entropy is $\,dS = \,dQ/T$ ...
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1answer
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Calculating heat absorbed from expanding gas [closed]

I'm trying to calculate the amount of heat absorbed per kg of different types of gas, namely compressed air and carbon dioxide. Starting with carbon dioxide, I found that the Joule-Thompson ...
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Function describing an adiabatic process

I understand that an isothermic process, plotted on a PV diagram, can be described by a rectangular hyperbola. However, now I am wondering, what about an adiabatic process, what function best ...