18
votes
Accepted
Formula for molar specific heat capacity in polytropic process
That $C$ is the specific heat for the given cycle, i.e.
$$dQ=nCdT$$
This is for $n$ moles of gas.(not the $n$ you stated in question)
I will assume $$PV^z=\text{constant}$$
$$nCdT=dU+PdV$$
$$\int nCdT=...
- 1,782
18
votes
Accepted
Why are sound waves adiabatic?
For starters, to quote Allan Pierce in Acoustics,
The often stated explanation, that oscillations in a sound wave are
too rapid to allow appreciable conduction of heat, is wrong.
That one ...
- 407
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 ...
- 14.8k
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 ...
- 16k
8
votes
Accepted
What is the difference between reversible and irreversible adiabatic expansion?
The difference is that one expansion is quasi-static (the reversible one) while the other is spontaneous because of a dramatic change of the external constraints (the irreversible one).
In the quasi-...
- 6,736
8
votes
Accepted
Adiabatic theorem and Berry phase
The adiabatic theorem is required to derive the Berry phase equation in quantum mechanics. Therefore the adiabatic theorem and the Berry phase must be compatible with one another. (Though geometric ...
- 2,628
8
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....
- 56.1k
8
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 ...
- 56.1k
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 ...
- 10.4k
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 ...
- 711
6
votes
Accepted
Adiabatic expansion in van der Waals gas
The correct answer is $(V-Nb)T^{C_V/Nk}=\text{const}$, the problem statement is just wrong.
- 96
6
votes
Sources to learn about Berry phases and Adiabatic Theorem
I suggest the American Journal of Physics as a good reference for undergraduates. The readership is Physics teachers so usually covers the topics that are of interest to students and the parts of a ...
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$$
Since $C_p -C_v =R$ and $\gamma= \frac{C_p}{...
- 1,415
6
votes
Where does the heat come from when rubber is stretched adiabatically?
Rubber is pretty damn complex!
On a macroscopic level, you do work to the rubber and it heats. When the rubber does work back, it cools. Just like when you compress a gas and then the gas expands.
The ...
- 6,093
6
votes
How to understand the quantum adiabatic theorem intuitively?
Imagine a Hamiltonian of the form $\hat H = \hat H_0 + \lambda \hat V$ where $\hat V$ is not assumed to be small. If $\lambda = 0$, then we can find a set of energy eigenstates $|\psi_{n}\rangle$ ...
- 51.8k
5
votes
Accepted
Condition for adiabatic approximation, derivation?
If you're willing to accept a perturbative argument, Shankar's QM book has a nice bit about this:
Take a Hamiltonian of the form:
$H(t)=H_0+e^{t/\tau} H_1$
Time-dependent perturbation theory says ...
- 7,002
5
votes
Accepted
Are all reversible processes adiabatic?
The formula for the change in entropy
$$
\mathrm{d}S = \frac{\delta Q_\mathrm{rev}}{T}
$$
refers to the entropy change of the system. For a reversible process the total change in entropy of the ...
- 7,652
5
votes
Accepted
Adiabatic Quantum Computing: why not just set the system in its problem Hamiltonian $H_{P}$ immediately?
I once asked the exact same question during a course on quantum computation. Systems only "fall into" their ground states when they are in thermal equilibrium at zero temperature. Both of these ...
- 41.5k
5
votes
Accepted
Please help to verify the solution and the contradiction
This is a particularly complicated problem to resolve. We encountered a similar problem on Physics Forums at the end of 2019 and into 2020, and another member named Andrew Mason worked with me to ...
- 27.9k
5
votes
Accepted
Does this violate 2nd law of thermodynamics?
The second law leads to (or can be stated)
$$
\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 ...
- 47k
4
votes
Accepted
Schrodinger basis kets with Time-dependent Hamiltonian
The basis of the Hilbert space in Schrödinger's picture is assumed to be time-independent regardless of any properties of the Hamiltonian. The Hamiltonian is just another operator. If the Hamiltonian ...
- 173k
4
votes
Infinite quantum well width $L$ to $2L$ adiabatic process
After the process ends, the new energy levels will be just the normal energy levels of infinite quantum well with width 2L.
moreover,
by the Adiabatic theorem:
A physical system remains in its ...
- 1,295
4
votes
Accepted
Why the air is more compressed near to the ground
If you have a glass of water, every molecule of water is under the influence of the gravitational potential field. Each molecule pushes down on the molecules below. The molecules of water near the ...
- 1,088
4
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 ...
- 6,157
4
votes
Accepted
Why is $C_{V}$ allowed in this equation $\Delta E_{int} = nC_{V}\Delta T$ for an adiabatic process?
The internal energy of an ideal gas is a function only of temperature. So, for an ideal gas, it doesn't matter whether the volume is constant or not. The subscript v refers to how $C_v$ of a gas can ...
- 27.9k
4
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 ...
- 34.4k
4
votes
Accepted
Why doesn't reversible adiabatic expansion generate heat?
I like this question! We rarely think about these processes so explicitly, but they can teach us a bit about what's going on microscopically. I'll consider a very concrete model and solve it.
Let's ...
- 95.3k
4
votes
Accepted
Does a fast process always have to be adiabatic?
If a process is rapid enough that there is little heat transfer between system and surroundings then treating it as adiabatic serves as a good first approximation (an adiabatic process strictly ...
- 6,157
4
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 ...
- 56
4
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 ...
- 27.9k
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