15
votes
Accepted
Why the entropy change is not zero in the irreversible adiabatic process?
Although entropy change is defined in terms of a reversible differential transfer of heat divided by the temperature at which the heat is transferred, you can have entropy change without heat transfer....
- 75.9k
14
votes
Why isn't the free expansion of a gas in an adiabatic container isentropic?
The free expansion isn’t reversible because the gas flows down a pressure gradient (that arises when you remove the piston). Any energy flow down a gradient generates entropy.
In contrast, during the (...
- 27.1k
12
votes
Accepted
Entropy change in the free expansion of a gas
What am I missing ?
Entropy can be generated without there being heat transfer, i.e., when $Q=0$. That's the case for a free expansion into a vacuum. The classic example given is an ideal gas located ...
- 75.9k
9
votes
How is ideal gas law applicable to real gas?
Ideal gas law works best for monatomic gasses at low pressures and high temperatures.
It doesn't take into account molecular size and intermolucular interactions, so when the effects of those are ...
- 15.3k
9
votes
How is ideal gas law applicable to real gas?
The speed of sound is defined as $c^2 = \frac{\partial p}{\partial \rho}$, which for an ideal gas becomes $c^2 = \gamma \frac{p}{\rho}$.
For a real gas, the relationship to an ideal gas can be found ...
- 16.7k
8
votes
Is there a generalization of the adiabatic theorem into a degenerate Hamiltonian?
Yes there is. Naturally these degeneracies should be motivated by symmetry considerations or else they would typically destroyed by perturbations. In particular, to have non trivial irreducible ...
- 13.5k
7
votes
Adiabatic Quantum Computing: why not just set the system in its problem Hamiltonian $H_{P}$ immediately?
Most NP-complete problems can be formulated as finding the ground state of some Hamiltonian. If you create a physical system that has such a Hamiltonian, it will be a "frustrated system". It will ...
- 11.4k
7
votes
Accepted
Rigorous Laughlin pumping argument
I solved the issue. I will explain in detail how the existence of an operator conserved by the adiabatic evolution allows us to make sense of the spectral flow argument.
Let's start with the problem ...
- 781
7
votes
Why the entropy change is not zero in the irreversible adiabatic process?
If you have an irreversible adiabatic process between two thermodynamic equilibrium end states of a system, there exists no possible reversible adiabatic process between these same two end states. So ...
- 34.3k
7
votes
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
isoentropic.
An adiabatic process is not isentropic unless it is also reversible. To be reversible, it must be carried out quasi ...
- 75.9k
7
votes
Accepted
Question regarding Adiabatic Process
In an adiabatic process, that is a process in which mathematically
$dQ=0$, $PV^γ=\text{constant}$.
First of all, the equation only applies to an ideal gas undergoing a reversible adiabatic process. ...
- 75.9k
6
votes
Why is $PV^\gamma$ constant in an adiabatic process?
For an ideal gas
$$PV=RT$$
Since
$$dU=dQ-dW$$
For adiabatic process
$$C_v dT = -{PdV}$$
Substituting $R dT = VdP+PdV$
$$VdP = -\frac{(R+C_v)}{C_v}PdV$$
Since $C_p -C_v =R$ and $\gamma= \frac{C_p}{...
- 1,520
6
votes
Two gases separated by a movable piston in a cylindrical container
Assume the initial volume on either side of the piston to be $V$.
After the piston is released and we allow everything to come to thermal equilibrium (the temperature is then $T$ on both sides), the ...
- 35.4k
6
votes
Accepted
Explanation of the diabatic basis
Recently, I have also came across this definition. Somehow, the concept is poorly explained in recent literature. Therefore, I went back to the original Zener's paper:
Proc. R. Soc. Lond. A 1932 ...
- 76
6
votes
Accepted
Adiabatic Process: Fast or Slow?
In Thermodynamics parlance, an adiabatic process is one in which there is no exchange of heat between the system and its surroundings. One way of accomplishing this is to have perfect insulation ...
- 34.3k
6
votes
Where does the heat come from when rubber is stretched adiabatically?
Rubber is pretty damn complex!
On a macroscopic level, you do work to the rubber and it heats. When the rubber does work back, it cools. Just like when you compress a gas and then the gas expands.
The ...
- 7,914
6
votes
How to understand the quantum adiabatic theorem intuitively?
Imagine a Hamiltonian of the form $\hat H = \hat H_0 + \lambda \hat V$ where $\hat V$ is not assumed to be small. If $\lambda = 0$, then we can find a set of energy eigenstates $|\psi_{n}\rangle$ ...
- 70.5k
6
votes
Why adiabatic expansion happens in Carnot cycle?
in $B \rightarrow C$, the working substance is isolated, and thus $Q =
> 0$, so $\Delta E_{int} = W$ where $W$ is the work done by the
environment to the system, not work done by the environment on ...
- 75.9k
6
votes
Accepted
Understanding the use of $d$ and $\partial$ in thermodynamics
The partial and total derivatives are different things, but they are related via the Chain Rule:
For $f(x,y,z)$, the differential of $f$ is:
$$df = \frac{\partial f}{\partial x}dx+\frac{\partial f}{\...
- 10.2k
5
votes
Accepted
Can a process be adiabatic and isobaric? Or Isovolumetric? Or isothermal?
If your system consists of single component, single phase substance, then its thermodynamic state is completely determined by specifying any two of its state variables. Therefore, a process cannot ...
- 6,574
5
votes
Accepted
Are all reversible processes adiabatic?
The formula for the change in entropy
$$
\mathrm{d}S = \frac{\delta Q_\mathrm{rev}}{T}
$$
refers to the entropy change of the system. For a reversible process the total change in entropy of the ...
- 9,316
5
votes
Adiabatic piston: why is Callen's argument flawed?
What is meant by
It was then noted that Callen's argument, which was repeated by Leff,
could not be correct since the equilibrium condition was derived from
the first law, rather than the second law.
...
- 797
5
votes
Accepted
Adiabatic Quantum Computing: why not just set the system in its problem Hamiltonian $H_{P}$ immediately?
I once asked the exact same question during a course on quantum computation. Systems only "fall into" their ground states when they are in thermal equilibrium at zero temperature. Both of these ...
- 48.8k
5
votes
Accepted
Please help to verify the solution and the contradiction
This is a particularly complicated problem to resolve. We encountered a similar problem on Physics Forums at the end of 2019 and into 2020, and another member named Andrew Mason worked with me to ...
- 34.3k
5
votes
Entropy change for an irreversible process
In an adiabatic irreversible process, entropy is generated within the system, and there is no transfer of entropy to the surroundings because heat cannot flow out. Thermally, the surroundings do not ...
- 34.3k
5
votes
Accepted
Does this violate 2nd law of thermodynamics?
The second law leads to (or can be stated)
$$
\Delta S_{\rm tot} \ge 0
$$
not $\Delta S_{\rm tot} > 0$ (where 'tot' refers to everything that undergoes some change during the given process). The ...
- 60.2k
5
votes
Accepted
Why does an elasticity approach for an adiabatically compressed bubble give a different answer?
There is indeed a problem with the energy expression $KV\varepsilon^2/2$. The problem lies in the derivation step $V\sigma\,d\varepsilon=VE\varepsilon\,d\varepsilon$, which relies on the Hooke's Law ...
- 27.1k
5
votes
Instantaneous eigenstate and time dependent Schrodinger equation
I think the easiest way to see this is with an example. Consider a Hamiltonian that changes suddenly at $t=0$
\begin{align}
H(t) = \begin{cases} H_1 & t \le 0 \\ H_2 & t > 0 \end{cases}
\...
- 9,316
5
votes
Accepted
Instantaneous eigenstate and time dependent Schrodinger equation
The point made by Zweibach in those notes is true even for time-independent Hamiltonians.
Let $\psi:\mathbb R\rightarrow \mathscr H$ be a trajectory through the Hilbert space $\mathscr H$, where $\psi(...
- 70.5k
5
votes
Why is the value of the heat capacity ratio $\gamma$ never less than 1?
During constant volume heating, the gas's volume is fixed, and hence it does no work on its surroundings. During constant pressure heating, the gas is allowed to expand against its surroundings, ...
- 8,414
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