Questions tagged [adiabatic]
Thermodynamic processes that occur without exchanging heat between the system and its environment.
448
questions
0
votes
1
answer
33
views
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=-\...
- 93
0
votes
1
answer
35
views
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 ...
- 41
0
votes
3
answers
57
views
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 ...
2
votes
0
answers
46
views
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 $|g_1\rangle$, $|...
- 2,586
0
votes
0
answers
22
views
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 ...
- 1
1
vote
1
answer
124
views
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)....
- 7,023
1
vote
1
answer
23
views
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 ...
- 121
3
votes
0
answers
75
views
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 ...
- 7,280
1
vote
2
answers
46
views
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 ...
- 11
2
votes
1
answer
154
views
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 ...
3
votes
2
answers
316
views
A problem involving adiabatic expansion of ideal gas
I am interested in answering the question which has nothing to do with a "homework". The question has also no aim to "check my work" because I have no doubts in my calculations and ...
- 286
1
vote
0
answers
67
views
Order $\epsilon^2$ mean rate of change in action variable for adiabatic oscillator
In adiabatic theory of classical mechanics, considering a linear oscillator with a slowly changing frequency $\omega=\omega(t)$, Percival and Richards's nice book (pp. 144-147) discusses how it is ...
- 612
2
votes
2
answers
68
views
How does speed of a thermodynamic process determine its type(adiabatic or isothermal)?
The part explaining adiabatic process in this answer says that,
In reality, adiabatic processes are approximations. They work best with systems that are almost isolated, but have a limited way of ...
- 1,158
3
votes
0
answers
34
views
When applying the adiabatic theorem, why doesn't the gap become doubly exponentially small generically?
Suppose we have a parameterised family of Hamiltonians $H(s)$, $s\in [0,1]$, acting on $n$ spins/qubits. When applying the adiabatic theorem, it is well known that if we wish to remain in the ground ...
- 687
3
votes
2
answers
2k
views
Behavior of air in a submersible implosion
I hope that this community could help to clarify some unproven but widespread claims regarding the implosion of the Titan submersible.
Background: The 2023 Titan submersible incident created a wide ...
- 39
1
vote
1
answer
42
views
Relation of first adiabatic exponent to adiabatic index
I'm going through a fluid dynamics text and I'm a little confused by a listed relation. The first adiabatic index is defined as
$$ \Gamma_1 = \left(\frac{\partial \ln P}{\partial \ln \rho}\right)_s, $$...
- 462
8
votes
1
answer
154
views
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 ...
- 177
0
votes
1
answer
47
views
A problem on adiabatic process [closed]
I solved this using the relation PV^gamma = constant (since it's an adiabatic process) and solved for the ratio of volumes. The answer key has, however, proceeded with delta U + delta Q = 0. The ...
0
votes
4
answers
56
views
Is there an equivalent of "adiabatic" for work (i.e. a workless transformation)?
In Fermi's Thermodynamics (1937), Chapter I, §1, he defines an isochore transformation as
a transformation during which the system performs no external work
He then discusses the case where the ...
- 166
0
votes
3
answers
148
views
Why can't entropy decrease for an adiabatic and closed system?
In equations (10) and (11) of this article by Curzon on the adiabatic piston, Curzon uses that a system which is thermally insulated cannot have its entropy decrease (irrespective of anything else ...
- 1,135
1
vote
1
answer
42
views
Determining an adiabatic gas coefficient
Is it possible to determine the adiabatic gas coefficient of an ideal gas when measuring the pressure of the gas in an isothermal process?
3
votes
3
answers
122
views
Are there known conditions that ensure infinite slowness is reversible?
A system has a Hamiltonian that depends on a few external parameters $V,X_1,X_2...$.
$$H=H(V,X_1,X_2....).$$
We can assume the dependence is continuous enough. A process is in the limit of infinite ...
- 551
-3
votes
4
answers
141
views
Derive $ΔS = Nk\ln(V/V_0)$ using fundamental equations of thermodynamics [closed]
I am considering a system with an ideal gas undergoing an adiabatic expansion. The initial volume is $V_0$ and final is $V$.
From this, How do I derive $\Delta S = Nk\ln(V/V_0)$ using fundamental ...
- 35
0
votes
1
answer
37
views
Why can't we use the time-dependent Schrödinger equation twice in the adiabatic approximation derivation?
In the standard derivation of the adiabatic approximation (see Sakurai in Modern Quantum Mechanics, Wikipedia) a differential equation for the coefficients is reached as
$$
i\hbar \dot{c}_m(t) + i\...
- 572
2
votes
2
answers
37
views
Can't we draw an indicator diagram for a fast adiabatic process?
We know that an indicator diagram can be drawn for an quasi static process only. An fast process in which there is no sufficient time for the exchange of heat can consider to be adiabatic. Can i draw ...
1
vote
0
answers
32
views
Adiabatic theorem for stochastic time-dependence
I am trying to derive the adiabatic theorem when my time-dependent Hamiltonian is stochastic and I have a few questions. Usually, one starts with the Schrödinger equation
\begin{equation}
i\frac{d |\...
- 65
1
vote
1
answer
108
views
How to take the average of a stochastic differential equation?
I am solving a set of stochastic differential equations and I need some feedback about if what I am doing is correct.
Given a vector $\boldsymbol{C}(t)=(C_+(t),C_-(t))^T$, we can writte a set of ...
- 65
0
votes
0
answers
53
views
What is the theoretical limit of adiabatic lapse rate as derived in introductory books?
In meteorology, the Earth's atmosphere up to the stratosphere is subject to processes that are, to a good approximation, adiabatic in nature.
Based on the state equation of an ideal gas, the adiabatic ...
- 997
0
votes
1
answer
54
views
Adiabatic theorem with stochastic variables
Suppose a system which is driven by a stochastic complex variable $\alpha$(t). Looking at the eigensystem, both eigenvectors and eigenvalues are then stochastic variables. In my case, after building a ...
- 65
1
vote
1
answer
29
views
Where does the lower limit of the integral for the dynamic phase factor come from? [closed]
I'm working on a problem right now where we have to figure out the transition probability between arbitrary excited states of the harmonic oscillator under a small time-dependent perturbation. Its ...
- 11
0
votes
1
answer
80
views
Determining the pressure after an adiabatic compression
(Please avoid explaining it with calculus)
I need to determine the pressure of air after an adiabatic compression. I have been given a low starting temperature T1 and a high final temperature T2 and ...
- 15
1
vote
4
answers
460
views
Why can't a heat engine have 100% efficiency?
Using the idea of isotherms and adiabats, I came up with the following argument to convince myself. First imagine the working gas within the system being heated along an isochore (hence all heat ...
- 45
3
votes
2
answers
141
views
Adiabatic compressibility always positive
I am currently studying statistical physics. Intuitively it is clear to me that the adiabatic compressibility $\kappa_s = - \frac{1}{V} \left(\frac{\partial V}{\partial P}\right)_{S}$ is positive in a ...
- 31
0
votes
2
answers
58
views
In the adiabatic theorem, how do we know which eigenstate we start on? (STIRAP)
I am aware of the question here, but it doesn't have an answer and also doesn't answer my question. I'm wondering about a specific case in STIRAP, where the 3 eigenstates are $$|\Psi_\pm\rangle = \...
- 664
2
votes
2
answers
53
views
How do we maintain polytropic processes?
In polytropic processes for an ideal gas,
$$PV^{\alpha}=constant$$ where $\alpha \neq 0,1,\gamma$
And $\gamma$ is adiabatic exponent of gas
So, how these processes are maintained?
What things are done ...
- 165
0
votes
1
answer
66
views
In adiabatic process, is work done in compression is equal to the work done in expansion? Please suggest
Assume a reversible adiabatic process where is there no exchange of heat from cylinder to environment. I assume that the work done on the system will be equal to the work done by the system. So, the ...
1
vote
0
answers
35
views
Adiabatic theorem for a 3-level system
If I have a 2-level system, with the energy splitting between the 2 levels $\omega_{12}$ and an external perturbation characterized by a frequency $\omega_P$, if $\omega_{12}>>\omega_P$ I can ...
- 521
2
votes
0
answers
56
views
Significance of Berry's phase
I'm familiar with the adiabatic theorem and have basic knowledge of quantum mechanics. While doing some independent learning, I stumbled on the concept of Berry's phase.
I would like to understand the ...
- 155
0
votes
1
answer
74
views
Joules expansion and piston kinetic energy
Say I have the original Joules expansion with an ideal gas, but I don't entirely neglect the piston. It can still be considered very light, but we can't neglect its kinetic energy in the process. How ...
0
votes
2
answers
421
views
Why is the final temperature of irreversible adiabatic processes higher than that of reversible adiabatic processes?
Suppose an irreversible adiabatic expansion process and a reversible adiabatic expansion process are starting from the same initial state, say, P1V1. Now, let both of these processes have equal ...
- 103
0
votes
1
answer
73
views
Adiabatic Exponent for an adiabatic process
Suppose we have some thermodynamic system, not necessarily a classical ideal gas, where
$$EV^{\gamma -1} = f(S,N)$$
Then for a process with constant $S, N,$ we have that
$$EV^{\gamma -1} = \rm const.$$...
- 2,143
1
vote
0
answers
23
views
What is adiabatic transfer?
In the context of atomic/quantum states preparation, what does adiabatic transfer mean? I'm currently reading about atom preparation using lasers and they talk about using adiabatic transfer to obtain ...
- 11
2
votes
0
answers
50
views
Physical effects of large detuning conditions in adiabatically eliminates cavity mode? [closed]
A simple question: how to adiabatically eliminates cavity mode in this thesis: here is arXiv/journal link of it page2, just above equation (2):
such that we can adiabatically eliminate the cavity ...
- 23
1
vote
1
answer
53
views
What is the entropy of the system, surroundings, and universe of a reversible adiabatic process?
I had a homework question that confused me a little bit. We were told to find the change in entropy of the system and the universe of a process. This process is an adiabatic, reversible process. From ...
- 13
1
vote
2
answers
99
views
Understanding page 141 of Blundell’s Concepts in thermal physics
On this page (in the second edition), there is a figure containing two states A and B of a system:
There are two paths between A and B: one is an irreversible change, and the other is a reversible ...
- 1,288
6
votes
5
answers
1k
views
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 ...
- 1,535
0
votes
2
answers
56
views
How does the adiabatic coefficient $γ$ vary with temperature (200K-20000K)? [closed]
At high temperatures, such as those encountered in hypersonic flight, γ varies a lot. My problem is that I can‘t find a graph accompanied by an explanation as to how & why it changes under ...
2
votes
0
answers
73
views
Adiabatic equation of state for a star
I am a little confused. To describe stars the adiabatic equation is often used: P = k$\rho^{\gamma}$. For a monatomic gas, the following holds: $\gamma = \frac{5}{3}$.
However, since the sun is not ...
- 31
0
votes
0
answers
27
views
Adiabatic Transformations and ideal gas relations
For an adiabatic transformation of an ideal gas I know that from equation,
$C_v=\frac{dU}{dT}$
I can rewrite it using the relations,
$dU=dQ-dW$
which can give us
$dU=-pdV$
to rewrite the first ...
- 73
0
votes
3
answers
67
views
Thermodynamic adiabatic process, question regarding mathematical operations
I have a question regarding mathematical operations often seen in physics books:
In an adiabatic process the heat is 0, so by the first law of thermodynamics we have that $E = W$, and an infinitesimal ...
- 11