Questions tagged [adiabatic]
Thermodynamic processes that occur without exchanging heat between the system and its environment.
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Thermodynamics exercise on transformations
An exercise in my book states the following:
n = 0.42 moles of an ideal biatomic gas are stored in an adiabatic cylinder with volume $V = 10^{-2} \text{ m}^3$, with an initial pressure equal to one ...
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Adiabatic Approximation in the spin 1/2 System
I am studying the following Hamiltonian:
$$H(t) = \begin{bmatrix}
\frac{t\alpha}{2} & H_{12} \\
H_{12}^* & -\frac{t\alpha}{2} \\
\end{bmatrix}$$
I want to assume that $\...
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Is the increase in the internal energy of an ideal gas equivalent to an increase in thermal energy?
ΔU = Q - W
Q: Heat received by the gas from the surroundings (positive if received, negative if given to the surroundings)
W: Work done by the gas on the surroundings (positive if done on the ...
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Finite-time effects in Landau Zener
Consider a two level system with a Landau-Zener Hamiltonian of the form
$$\hat{H}=\begin{pmatrix}v t&\beta\\\beta&-v t\end{pmatrix}.$$
The Landau-Zener formula provides a closed form for the ...
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Entropy in irreversible adiabtic process
We know that,
$$dS=\dfrac{\delta Q_{rev}}{T}$$
If you have an irreversible adiabatic process between two thermodynamic equilibrium end states of a system, there exists no possible reversible adiabatic ...
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Adiabtic aproximation and MSW effect
I have been reading about the MSW effect in neutrinos from supernovae. In some papers, it's assumed the "adiabatic case" which, according to the book "Neutrino Physics and Astrophysics&...
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Origin of ideal gas fluid dynamics equations including the adiabatic index
I was given a system of equations that supposedly describes the fluid dynamics of an ideal gas.
The equations are:
$$
\begin{align}
&\frac{\rho}{m} = \frac{p}{T} &\text{(ideal gas law)} \\\\
&...
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Modelling the number of times a gas tank can be filled
I'm currently working on a project where I need to estimate how many times a large, high-pressure gas tank can refill a smaller tank. For this purpose, I'm using a pressure regulator to manage the ...
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Constructing a gapped family of Hamiltonians in the trivial paramagnet
Consider the trivial paramagnet, which has the Hamiltonian $$H = - \sum_i \sigma^x_i$$ Now let's say I have two different Hamiltonians $$H_0 = H + 2\sigma^x_{i_0} \qquad H_1 = H + 2\sigma^x_{i_1}$$ ...
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Given state $P$, does the set of all forward adiabatic processes and reversed adiabatic processes reach all states in the state space?
Let $A$ be a thermodynamic system and let $\Sigma$ be its state space. By the state postulate, if $A$ has $n$ two-way work channels (i.e. ways in which work can be done both positively and negatively ...
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Why doesn't $\gamma = \frac{5}{3}$ for all adiabatic processes
For monoatomic, ideal gases, $PV^{\frac{5}{3}}$ is constant. I have been told that this does not hold for diatomic, or other non-monoatomic gases. However, I derived the relationship using only the ...
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Why slow compression with conducting walls should be isothermal?
I know that for an isothermal process heat transfer is necessary so process should be slow and walls should be conducting for heat transfer to occur as a process cannot be isothermal and adiabatic at ...
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Bit structure in Adiabatic Quantum Computing [closed]
https://arxiv.org/pdf/quant-ph/0007071.pdf
In Chapter 6 in the paper "A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability”, by Edward Farhi, Jeffrey ...
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Non-adiabatic evolution and time-dependent adiabatic parameter
I am dealing with the dynamics of a two-bands lattice system. The idea is that you have a lattice model of free fermions, with some hopping amplitudes and on-site energies.The lattice have two fermion ...
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Derivative of $c(t)$ in Adiabatic Approximation
In Sakurai's Modern Quantum Mechanics, second edition, $5.6.10$ is
$$\begin{aligned}
\dot{c}_m(t)=-\sum_nc_n(t)e^{i[\theta_n(t)-\theta_m(t)]}\langle m;t|\left[\frac\partial{\partial t}|n;t\rangle\...
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What is the relation between the Adiabatic Approximation used in quantum chemistry and the one given in QM textbooks?
I am an aspiring quantum chemist and have come across two vastly different versions of the Adiabatic Approximation when studying Quantum Mechanics from the perspective of physics and chemistry ...
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Finding condition for Adiabaticity
I have a differential equation describing a resonator that looks like this:
$$ \frac{d\alpha(t)}{dt} = [j a - b]\alpha(t) + \sqrt b e^{jct}$$ where I can solve it putting: $$\alpha(t) = \alpha e^{jct}$...
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Why is an adiabat steeper than an isotherm in a $p$-$V$ curve?
What I have so far gathered is a mathematical explanation.
Since for an adiabatic process, $pV^γ=$ constant, for a unit change in pressure, change in volume would be very less. Therefore, if compared ...
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Why do we need an adiabatic expansion in the Carnot cycle? [duplicate]
As we know that 1st process is an reversible isothermal expansion during this the system is in quasi static equilibrium which helps in increasing the volume of the system but why does the second step ...
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Temperature increase in fixed volume due to gas injection
I have a vessel of fixed volume with adiabatic boundary which is initially filled with air at pressure of 1 atm and temperature of 300 K. Now, I inject air from an external source at a fixed flow rate ...
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Change in temperature due to adiabatic expansion against the vacuum
Let's consider an ideal gas that expands in vacuum and it is thermally isolated from the surroundings. Since it is isolated, it does not exchange heat with the exterior $Q=0$. Since it is expanding ...
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In an adiabatic process, if there is no heat flow between system and surroundings, then why don't we consider temperature to be constant always?
How can the temperature of a body change unless heat flows in or out of it?
So shouldn't all adiabatic process be considered isothermal too? but that is not true as both the processes have different ...
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Question about Landau's derivation of the energy relation in Statistical Physics (Vol 5)
In Statistical Physics (Vol 5 of Landau's books) section 11, Landau derives an important relation: $\overline{\frac{\partial E(p, q;\lambda)}{\partial \lambda}} = \left(\frac{\partial E}{\partial \...
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Container divided by adiabatic wall with mass and friction: why is it a quasi-static process?
Thanks to the help of @ChetMiller, the following fact is essentially concluded in this thread. Consider a rigid, thermally isolated container divided by a massless barrier parallel to its base into ...
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Container divided by frictionless adiabatic wall: reversible or irreversible process?
I have encountered an issue in the following physical situation. Consider a rigid, thermally insulated container divided by a barrier parallel to its base into two parts, left and right, each ...
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Is sound really adiabatic because it is a fast process?
In many books I have consumed so far there is the statement that sound is adiabatic because heat transfer does not have nearly enough time to reach isothermal equilibrium. Doesn't this contradict ...
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Reversibility of the ideal Carnot cycle
How do adiabatic processes in the reversible Carnot cycle take place? Is the gas adiabatically isolated? If so, how would that happen in real life? (I know that Carnot cycle is not practically ...
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How to model adiabatic lapse rate from first principles?
As a motivating example, consider that the grand canyon floor is ~11ºC warmer than the top. The dry adiabatic lapse rate of 9.8ºC/km, at the average depth of 1.2km deep, implies a 11.76ºC warmer floor ...
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Can we apply thermodynamics processes for real gas too? And how
Like in adiabatic process there is closed system but in reality we know there is no such thing as closed system there will be still exchange of heat so it will not work adiabatically means it is only ...
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Adiabatic expansion paradox [duplicate]
If we let a gas expand against vacuum with a piston which is not weightless then can we call it free expansion? If yes then there is a paradox . Work done by a gas is said to be = -p( external) ...
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Work done by adiabatic expansion derivation
I know that $W=-C_v(T_2-T_1)$ for an adiabatic expansion, and I know how to derive it. However, in this video (https://youtu.be/gaZmZjBtgAM?si=Px3v2qDG3CIdupgi&t=358) it mentions the formula $W=-\...
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Maxwell's relations and adiabats
I was trying to understand problem regarding finding the adiabatic modulus given the isothermal young's modulus. I'm still an amateur in thermodynamics.
I just didn't understand the final step where ...
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Why does adiabatic expansion occur in the Carnot cycle?
Several people have asked this question before and I haven't found any of the explanations even remotely satisfying.
To begin, Let's imagine our system consists of an ideal gas enclosed in a cylinder ...
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Understanding adiabatic elimination in three-level system coupled to EM field
I am having some difficulties understanding the "adiabatic elimination" in the context of atomic physics.
In particular, consider a three-level system with states labeled by $|g_1\rangle$, $|...
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Effect of Uniform Motion on Internal Energy of an Ideal Gas in an Isolated container [duplicate]
“The internal energy of a gas contained in a beaker is U, if the box starts moving with velocity V, then internal energy of the gas will be...”
Elaboration
So, further explaining the situation, we ...
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How to prove that $\gamma \le 2$ for *causal* relativistic polytrope fluids?
The definition of the adiabatic index of a relativistic polytrope fluid is this:
$$\tag{1}
\gamma = \frac{\rho + p}{p} \, \frac{dp}{d\rho},
$$
where $\rho$ is the energy density (not the mass density)....
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The work and reversibility of an adiabadically stretched band
I currently working on this. More specifically I have a question about Problem 2.8 (solution on page 34 and exercise on page 25 of the pdf). I have 4 questions
1.
In the solution for b) the author ...
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Implement Adiabatic Elimination on Hamiltonians?
Adiabatic elimination is the process of truncating a Hamiltonian's Hilbert space to the "slow" states you care about. You throw out the "fast" eigenstates to produce a smaller ...
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Adiabatic free expansion into vacuum
Consider an adiabatic vessel with a partition and a plug in the partition wall. On one side of the partition, there is gas at certain pressure and on the other side of partition there is perfect ...
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Question regarding Adiabatic Process
In an adiabatic process, that is a process in which mathematically $dQ=0$,
$PV^γ=\text{constant}$.
Now my question is that do we have a value for this constant? This is because just like for ...
