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Questions tagged [chemical-potential]

Chemical Potential; which is a form of potential energy that can be absorbed or released during a chemical reaction applies to questions in thermodynamics where a chemical potential is the subject of the question.

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Deriving Ohm's law from Sommerfeld's free electron gas

I am reading this post and in particular Mike Stone's answer How does he end up in the conclusion that the wavefunction of the free electron gas model is $\sqrt{\rho}e^{ikx}$?
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How does the Fermi level of graphene change if it is placed in a biased pn junction or in a plate capacitor?

I ran into a problem on which I can't really find any solutions in literature. I am looking at a Graphene sheet that is sandwiched in a biased pn junction (current flows orthogonal to the Graphene ...
kimcheez's user avatar
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A problem to find the the chemical potential from the free energy (Ginzburg-Landau/Cahn-Hillard)

I have a problem to derive exactly the spatial term of the chemical potential from the free energy of the Cahn-Hillard equation So, let us start with the free energy of a binary mixture (A and B). The ...
math-int's user avatar
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Determining free Fermi/Bose gas chemical potentials, given temperature, number density, and baryon density

I'm attempting to recreate some plots of individual particle chemical potentials from S. Reddy et. al.'s paper on neutrino interactions in hot and dense matter (of the same title). The specifics aren'...
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Change in internal chemical potential of electrons in the 2DEG

I was reading about quantum capacitance and came across the following formula: $$\Delta \mu = \frac{N}{\rho}$$ where N is the number of electrons moved from the metal to the low-density-of-states ...
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Chemical Potential of a Fermionic System

If the chemical potential of a fermionic system is $0$ at temperature $T=0$, will it be zero at any arbitrary finite temperature?
Snpr_Physics's user avatar
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Average number of particles in a Fermi gas

I want look (and plot) how the average number of fermions depends on temperature and the chemical potential. According to Eq.(13.12) in https://itp.uni-frankfurt.de/~gros/Vorlesungen/TD/...
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Determining the single particle energies in a neutrino opacity calculation

I'm attempting to recreate some plots from this paper on neutrino opacity calculations for interacting matter at supra-nuclear densities. Namely, I'm trying to write a Python script to perform the ...
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For intrinsic semiconductors, is the gap Energy equals $E_c-E_v$ or $E_c+E_v$?

So I have a problem with the intrinsic Fermi Level because by definition it is in the middle of the gap energy, and knowing that Eg=(Ec-Ev), we should have Ei=(Ec-Ev)/2. But when we follow the ...
anass bakour's user avatar
2 votes
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Chemical equilibrium for distinguishable reactant particles

Denote the partition function of a single particle by $\zeta$. The particles of one type of reactant in a chemical reaction are normally indistinguishable. The partition function of $n$ number of a ...
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Why are things electronegative and electropostive?

Chemical reactions happen because of electron donation. Atoms already have an equal amount of proteins and electrons, so they should cancel out and the atom should not have to steal/donate electrons. ...
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Is fuel cell efficiency limited by thermodynamics?

Let's say we have a mixture of oxygen and hydrogen gas, initially at room temperature and pressure. This mixture can be used to perform work: we can burn it, using the resulting heat as a source in a ...
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Temperature dependence of chemical potential in a semiconductor

My professor just uploaded the following two foils: and Now I understand that if temperature increases we have some electrons in the conduction band and some holes in valence band, which would (I ...
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Confusion about canonical and grand canonical ensembles regarding Fermi-Dirac statistics

All derivations I have seen for the Fermi-Dirac statistics presuppose the grand canonical ensemble. However, all applications of it, e.g. ideal quantum gases, electrons in a metal and semiconductors, ...
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Chemical Potential after Freeze-Out

I've been wondering what happens to the chemical potential $\mu$ of a particle (more specific, a fermion) with a mass m that freezes out around a temperature of $T\sim m$. I understand that the ...
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Definition of Fermi level

In wikipedia article, there is following sentence. The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually ...
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What's the difference in chemical potentials between nearly free electron model and tight-binding model?

In nearly free electron model, we know that when temperature is zero, the chemical potential $\mu$ is same as the Fermi energy $E_F$, $\mu=E_F$. For a good metal, $E_F$ is roughly $10\mathrm{eV}$, so ...
Houmin Du's user avatar
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Chemical potential of an ideal quantum gas

As far as I understand from textbooks, absolute values of the chemical potential are meaningless, only changes have physical meaning. That would mean that, from statistical mechanics, one should only ...
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Time evolution operator with chemical potential

In the Bruus and Flensberg textbook, section 1.5, it is mentioned that Basically, the result obtained from the canonical ensemble is carried over to the grand canonical ensemble by the substitution $...
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Constant shift in the Gibbs free energy

As far as I know, measurable thermodynamic properties (pressure, temperature, volume, etc.) all depend on derivatives of the thermodynamic potentials. For instance, $$1/T= (\partial S / \partial E)_{V,...
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Is the Fermi level taken to be (approximately) constant, i.e. equal to the Fermi energy, in semiconductor physics?

I have been reading Neamen's "Semiconductor Physics and Devices" Chapter 3. He derives in Eq. (3.79) the Fermi-Dirac distribution function $$f_F(E) = \frac{1}{1 + \exp(\frac{E-E_F}{kT})}, $$ ...
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What is the interpretation of the eigenvalues of $e^{-\beta (H-\mu N)}$?

In quantum statistical mechanics, the equilibrium state is characterized by a density matrix $\rho$. Let me focus on the grand canonical ensemble, although the question also holds for the canonical ...
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Can quantum tunneling of some sort allow 2 solids which dont touch each other to have the same chemical potential?

Suppose we have 2 solids seperated by a distance x.If the distance x is in the quantum range(10-20 atoms) even though the solids dont touch each other would their Fermi levels become the same after ...
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Which electrode potentials govern Lithium-ion batteries?

I have a very basic question on why Li+ ions move from anode to cathode during discharge of lithium-ion batteries. Others have asked, but the explanations don't give electrode potentials. what ...
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Chemical Potentials and Phase Changes [closed]

The Wikipedia article for the Helmholtz free energy has a derivation showing that if the volume and temperature of a system are kept constant, then $$W \leq - \Delta F$$ Where $W$ is the work ...
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How to understand chemical potential?

I wonder how to understand the chemical potential in terms of the condensed matter physics. Let’s say without the thermodynamic terms. Let’s consider some example system that can conduct and its ...
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Why doesn't $\mu$ change during a phase transition?

I am learning about (first-order) phase transitions from Callen's Chapter 9 and am a bit baffled about something. Some of the confusion may be related to my question 1) here, too. In the below, I bold ...
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How does evaopration and diffusion affect concentration of solute at the solvent surface?

Imagine a long, thin tube with one end sealed and the other end open. It is filled with a volatile solvent with a dissolved non-volatile solute. As the solvent evaporates at the liquid surface, the ...
YEp d's user avatar
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1 answer
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How do I interpret the chemical potential for hydrogen atoms in a neutral gas of hydrogen, protons and electrons?

I am currently self-studying the lecture notes of David Tong on Statistical Physics. In question 6 of problem sheet 2 (https://www.damtp.cam.ac.uk/user/tong/statphys/omg2.pdf) we are asked to find a ...
Nic Christopher's user avatar
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Chemical potential of ideal solution in grand canonical ensemble

I am attempting to derive the chemical potential of an ideal solution within the grand canonical ensemble. I know that the final answer should be (https://en.wikipedia.org/wiki/Ideal_solution) $$\mu_j=...
Greenhorn3.14's user avatar
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2 answers
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What does chemical potential really mean? [duplicate]

I do not completely understand the concept of chemical potential $\mu$: It is usually defined by $$\delta Q = T dS = dU + pdV + \mu dn$$ By adding, lets say 1 mole of mass to a gas of 10 moles ($\...
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4 answers
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Chemical equilibrium conditions for mixture of ideal gases vs. ideal gas separated by partition

I am not sure whether chemical equilibrium conditions are the same or different for the two scenarios below: i. Closed rigid container of volume $V$ with uniform temperature $T$ and pressure $P$ ...
Ray Siplao's user avatar
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1 answer
243 views

How it is possible for chemical potential of ideal gas to vary based on composition?

According to this post, $$\mu_i = g_i + RT \ln \frac{N_i}{N_1+N_2}$$ It shows that chemical potential indeed do vary with composition. I have trouble understanding how this equation is derived. I ...
Ray Siplao's user avatar
5 votes
2 answers
380 views

Do chemical potentials stay constant in chemical equilibrium?

I am uncertain whether chemical potentials stay constant during chemical equilibrium. Consider a closed container divided into two parts 1 and 2 filled with ideal gas particles. The barrier between ...
Ray Siplao's user avatar
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1 answer
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What are these two equations related to Maxwell-Boltzmann Distribution called? [closed]

I have come across these two equations on Maxwell-Boltzmann Distribution: and May I please know what the equations are called so I can read up more about them?
Yang Hao's user avatar
1 vote
2 answers
236 views

Intepretation of the Fermi Dirac distribution graph [closed]

Is there a significance or an important interpretation of the fact that the plots in the Fermi-Dirac distribtion graph, all intersect at the point with coordinates ($\epsilon_F$,$\frac {1}{2}$)? https:...
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How chemical potential for two systems change?

I was reading this notes about chemical potential. I am confused about some things in section 2: Potential energy and the chemical potential Let us look at two systems A and B a the same temperature ...
John Davies's user avatar
1 vote
1 answer
244 views

Proof that Fermi level is constant throughout a system in thermal equilibrium

The explainations I saw: The one I was referring to in this question. I described why I find this explaination not satisfying in the question. Consider $2$ systems in contact. The rate of particles ...
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2 answers
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Why chemical potential changes as a system approaches chemical equilibrium?

Consider a closed system of constant volume $V$, constant pressure $P$, temperature $T$, and Gibbs energy $G$ that is in thermal and mechanical equilibrium with surroundings. It is filled with $N$ ...
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Is there a "4th law of Energetics"? How is energy conserved in a stationary flow through a pair of semi-permeable membranes?

I asked this question but got no replies there. The below longish quote is from Rosenberg's Some Aspects on Brønsted's Energetic Theory. It concerns two chemical species, $A$ and $B$, in a stationary ...
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Why does the bottom of the conduction band correspond to the potential energy of an electron?

While proving that Fermi level is constant throughout any system in thermal equilibrium, all the books I saw the proof in (for example, Sze and Shur) assume the following: the bottom of the ...
Sgg8's user avatar
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Band insulators and the chemical potential

A quick question on the chemical potential in a band insulator. We all know that the chemical potential lies in the gap, which is fine, but the question is how can this happen exactly? My thoughts are ...
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Gibbs-Duhem equation and homogeneous function of mixed Euler order

My question is related to this article by Sorensen and Compan. The usual definition of an homogeneous function of order $\mathcal M$ is by the equation $f(\lambda \mathbf{x}) = \lambda^{\mathcal M} f(\...
hyportnex's user avatar
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Confusion regarding the definition of electrochemical potential

I am having trouble understanding the concept of the electrochemical potential $\mu$. In my textbook the electrochemical potential is defined as $\mu=\frac{\partial G}{\partial n}$. It seems to me as ...
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2 answers
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Where do the electrons that are filled up to the fermi level above the valence band go?

Many questions have been asked on this topic, but this has never been answered satisfactorily. Yet I want to give it a shot. Fermi Energy represents the energy level achieved when all the available ...
cashual-introspector's user avatar
3 votes
1 answer
97 views

Shouldn't $dU=TdS-PdV$ be true for every closed system?

For a closed system, if there aren't chemical reactions or a phase change inside it, $dU=TdS-PdV$ is the fundamental thermodynamic relation. This expression can be generalized, for a closed system ...
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Why does the depletion region in a reverse biased diode grow?

From what I understand, at the pn-junction of a diode, electrons diffuse from the n-region into the p-region until the resulting electric field grows large enough to stop any further flow of electrons....
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291 views

Chemical potential $\mu$ controls filling?

If total magnetization of a spin 1/2 system is zero, does it mean that system is at half filling? or chemical potential $\mu=0$? I was trying to show that chemical potential controls filling by taking ...
Barry's user avatar
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Chemical potential terms in Hamiltonian

In the derivation of grand canonical ensemble, which assumes that the physical system (with Hamiltonian $H$) has an average energy $E$ and an average number of particles $\bar{N}$, the density matrix ...
Zhengyuan Yue's user avatar
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Pseudo Van der Waals gases

In college, when deriving the Langmuir isotherm for gas-solid adsorption, it implied equalling the chemical potentials for a certain compound in the gas and the interphase, and when dealing with the ...
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