Thermodynamic processes that occur without exchanging heat between the system and its environment.

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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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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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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 ...
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### 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 ...
1 vote
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 $$\Gamma_1 = \left(\frac{\partial \ln P}{\partial \ln \rho}\right)_s,$$...
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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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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 $$EV^{\gamma -1} = \rm const.$$...
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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 ...
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### 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 ...
1 vote
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### 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 ...
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### 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 ...
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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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### 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 ...
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### 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 ...
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 ...
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 ...