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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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Statistical mechanics with a freely variable parameter

I would prefer to limit this question to the microcanonical ensemble for ease. I'm particularly interested in the limit that there is no intrinsic cost to introducing particles into a system, in the ...
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Why there is no chemical potential on this thermodynamic relation?

I was following the book by Landau and Lifshitz, Fluid Mechanics (2nd edition) and got stuck trying to understand one of their arguments. On the chapter about Relativistic Fluid Dynamics it is stated ...
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Usage of pure substance chemical potential for the mixture of gases

There is a known expression relating the change in the Gibbs energy of the ideal gas to the change in pressure under the constant temperature $T$: $$\Delta G = nRTln\frac{p_f}{p_i} \tag{1}$$ where $n$ ...
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Chemical potential and equilibrium condition

My question is about the $dG=0$ condition for the equilibrium in a system, say, solid + gas (water and ice, if you prefer). Almost every textbook gives the following recipe to understand phase ...
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By shortening the N-type side to the P-type side of a diode with a wire, how does the electric potential looks like in each point of this circuit?

To avoid misunderstanding I'll first start with the notions. The electrochemical potential (which in semiconductors refers to as the Fermi level) is the sum of the chemical potential and electrical ...
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127 views

Is BE condensation possible for photons, phonons and magnons all with $\mu=0$ (non-conserved particle number)?

Photons have zero chemical potential and their number is not conserved. The property of zero chemical potential is also true for emergent gapless excitations such as phonons in crystals and magnons in ...
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1answer
105 views

Grand canonical partition function of hypothetical particles

I have to calculate the grand canonical partition function of a system of hypothetical particles, wherein each single-particle quantum state can be occupied by up to 3 particles. Obviously this is a ...
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2answers
42 views

Determination of chemical potential

I've written a partition function for a problem $Z_1=e^{\mu+\beta\varepsilon_1}+2e^{\mu+\beta\varepsilon_1}$ and calculated the free energy for N particles $F=-kT\ln{Z_1^N}$. I'd like to get the ...
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Calculating free energy from partition function

So I have $N$ particles and I've determined the partition function for one of them to be $Z_1=\lambda e^{\beta\varepsilon_1} + 2\lambda e^{\beta\varepsilon_2}$. I know the free energy is $A=-kT\log(Z)$...
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How come chemical potential is $RT \ln c$?

For years, I just assumed that chemical potential μ is RT ln c. This equation is terribly important, as it helps calculate equilibrium in chemical reactions, electrochemical potentials over membranes, ...
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28 views

Finding the chemical potential of a system

For a system of non interacting electrons at temperature T the density of states is given by $$g(\epsilon)=\begin{cases}\sqrt{\epsilon-\epsilon_0} & \text{for }\epsilon > \epsilon_0 \\ 0 &...
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Entropy as a driver behind processes

I sometimes encounter explanations of phenomena where only entropy is quoted as a driver, for example, osmosis, diffusion, hydrophobic effect... But can entropy ever be the sole driver of a process? I ...
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1answer
37 views

Polyakov Loop and Chemical Potential

I have read in a paper (http://arxiv.org/abs/1203.3556) that in a thermal field theory, the chemical potential is $\mu=T \ln P$ where $$T^{-1}=\int_{0}^{\beta} \sqrt{-\xi^2}dt,$$ $\xi$ is $\partial_t$,...
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Definition of chemical potential of an ideal gas contradicts equation of state?

My geometric intuition breaks down horribly regarding advanced concepts in thermodynamics, such as the use of thermodynamic potentials. My question here is therefore about the latter concepts (in ...
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1answer
50 views

Chemical potential of graphene : is $1~\rm eV $ too high?

I am working on graphene plasmonics and I read the following paper that discusses graphene nanoantennas. https://www.osapublishing.org/oe/abstract.cfm?uri=oe-21-3-3737 They use a chemical potential ...
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74 views

Source of the Chemical Potential

I know that the chemical potential is the energy required to add another particle to the system but what is it's origin on the microscopic level? Take for example the case of the ideal Fermi gas, the ...
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Why the Fermi energy be approximated as the chemical potential at low temperature?

For the Fermi-Dirac distribution, $n(E)=\frac{1}{e^{\beta(E-\mu)}+1}$, why can we approximate the chemical potential, $\mu$, to be equal to the Fermi energy, $E_{f} = \mu(T=0) = k_{B} T_{f}$, when $T &...
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Chemical potential of solute in a saturated solution

It's been a while with my encounter with chemical potential. Now that I am studying a research paper, it somehow implies that the chemical potential of a solute under saturated solution (standard T, ...
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1answer
40 views

Why external chemical potential?

My thermal physics textbook written by Kitten says: When external potential steps are present, we can express the total chemical potential of a system as the sum of two parts: $$\mu=\mu_{tot}=...
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1answer
129 views

Why is chemical potential equivalent to a true potential?

My K&K thermal physics testbook says chemical potential is equivalent to a true potential: the chemical potential is equivalent to a true potential energy: the difference in chemical potential ...
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1answer
84 views

Thermodynamic potential of a solar cell

It is a known result that the photo-voltage generated in photovoltaic system (such as a simple p-n junction) is directly related to the quasi Fermi levels splitting at the contact - as illustrated by ...
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The role of the chemical potential in the Hubbard model

The third term of the Hubbard model $$H=-t\sum\limits_{<i,j>} \sum_\sigma c_{i,\sigma}^{\dagger}c_{j,\sigma} +H.c.+U\sum\limits_{i} c_{i,\uparrow}^{\dagger} c_{i,\downarrow}^{\dagger} c_{i,\...
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Chemical potential for ideal fermi gas with single particle energies $\epsilon_k^{\pm}=\pm \hbar c |\mathbf k|$

I came across the following question in some example problems for my graduate statistical mechanics course final exam: Consider an ideal gas of fermions of density $n$ in three dimensions with the ...
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1answer
57 views

Physical Intuition for thermodynamic limit of the average occupancy, $\langle N\rangle$, of an orbital

Say your allowed occupancies for an orbital are $0, 1, 2$, and the values of energy associated with these occupancies are $0, \epsilon, 2 \epsilon$. Give an expression for the ensemble average ...
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1answer
88 views

How can a chemical gradient oppose an electrical gradient?

I'm a physicist taking a class on cell biology and we are currently discussing the concept of an electrochemical gradient, the difference in potential (voltage) and chemical concentrations across a ...
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What's the meaning of chemical potential of photons or phonons?

The chemical potential of photons or phonons vanishes due to their particle number not conserved, I don't understand it very well. So can you expain what's the meaning of chemical potential of them ...
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Could you please give an intuitive definition of chemical potential?

Could you please give an intuitive definition of chemical potential? It seems that it is an extremely important notion of physics but definitions are really vague.
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275 views

Chemical potential in quantum field theories

The chemical potential enters the grand canonical ensemble, in statistical physics, as the Lagrange multiplier ensuring the conservation of particle number. In QFT and relativistic theories in ...
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1answer
54 views

Chemical Potential: sign of external potential energy

In statistical mechanics the total chemical potential $\mu _{\mbox{Total}}=\mu _{\mbox{Internal}}+\mu_{\mbox{External}}$. In the examples I have done so far $\mu_{\mbox{External}}$ is the external (...
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1answer
120 views

Voltage and Fermi levels

It is well known that the voltage $V$ across, say, a p-n junction can be related to the electro-chemical potentials (usually and improperly called Fermi levels) at the borders of the junction $$ qV = \...
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1answer
227 views

What happens to the partition functions in the limit $T\to 0$ or $\beta\to\infty$?

Consider the canonical and grand canonical partition functions given by $$Z_C=\sum\limits_{i}g(E_i)e^{-\beta E_i}$$ and $$Z_G=\sum\limits_{i}g(E_i)e^{-\beta (E_i-\mu)}$$ respectively with $\beta=\frac{...
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Electrochemical potential in 2D

I was calculating the electrochemical potential of a free electron gas using the Sommerfeld expansion, for a 2D case it turns out the electrochemical potential has a very simple form $\mu (T) = E_f$, ...
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1answer
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Temperature, Kinetic Energy, and Chemical Potential

I have a confusion that in an Homogeneous electron gas. When $T=0$, we know that $\mu=E_F$. So Kinetic Energy per electron=$\frac{3}{5}E_F=\frac{3}{5}\mu$. I thought that Temperature is related to ...
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1answer
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How to obtain $\mu\left(T,P\right)$ form the potential $U=\alpha\frac{S^4}{N^2V}$

I have this homework where i need to derive $\mu\left(T,P\right)$ from $U=\alpha\frac{S^4}{N^2V}$ where $\alpha$ is a constant positive, i've been trying some ways, one of them is using the Gibbs' ...
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$\alpha$ in the Grand Canonical Partition Function

When moving from the Canonical Partition Function to the Grand Canonical Partition function, we relax the restriction on the number of particles N by introducing the sum $$\mathcal{Z} = \sum_{N'=0}^\...
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Why zero chemical potential does not allow the Bose-Einstein Condensation of Phonons?

Here I report the reasoning from which my question comes. According to: O.V. Misochko, Muneaki Hase, K. Ishioka, and M. Kitajima. Transient bose–einstein condensation of phonons. Physics Letters A, ...
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Chemical Potentials, why is there N∂µ but no µ∂N?

I've been studying up on the thermodynamic potentials and I noticed that the four thermo potentials are combinations of the (T,S) and (p,V) pairs. Adding chemical potential adds a (µ,N) pair in the ...
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How could chemical potential be interpreted as the molar Gibbs free energy?

As known, the Gibbs free energy for a closed system at constant temperature $T$ and constant pressure $p$ (and thus constant volume $V$), $G=U+pV-TS$, will be minimized, where $U$ is the total ...
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164 views

Sommerfeld Expansion & Chemical Potential

I'm trying to show how the chemical potential depends on the temperature and i'm advised to use the Sommerfeld expansion. I'm using it on the density of charge $ n=\int^{+\infty}_{-\infty} \rho(\...
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An equation for chemical potential from the Boltzmann entropy equation

I am trying to derive an equation for chemical potential from Boltzmann entropy and this is what I have come up with so far: $$S = k\ln{\left(\frac{N!}{N_\mathrm{up}!\,N_\mathrm{down}!}\right)} \...
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444 views

Derivation of chemical potential using Boltzmann entropy and number of microstates [closed]

If one has the Boltzmann equation for entropy $$ S=k \ln(W) $$ where $$ W=T^{C/k}V^{N} $$ is the number of microstates, and it is assumed that all the particles are indistinguishable How would one ...
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1answer
347 views

QCD chPT chemical potential

I have recently been to a guest lecture about low energy QCD with a finite isospin chemical potential. I have two overall questions about this, since it wasn’t possible to ask questions at the given ...
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184 views

Reaction rates and chemical potentials

In this paper they consider the chemical reaction $P + R \leftrightarrow Q $, with $k_1$ and $k_2$ the forward and backward rates, respectively. The time evolution of the concentration [P] is $$ \frac{...
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Can we extract work from atmospheric hydrogen?

In a discussion about future passenger aircraft which aren't powered by fossil fuels, my friend suggested that powered flight may be possible using hydrogen harvested from the atmosphere. I claimed ...
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The chemical potential as the zeroth component of a constant gauge field

The chemical potential $\mu$, is introduced in the action as the lagrange multiplier $$ \tag 1 S[Q_{0}] \to S[\mu] = S[Q_{0}]-\int dt \mu Q_{0}(t), $$ where $$ Q_{0}(t) = \int d^{3}\mathbf r J_{0}(\...
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Effective field theory with coordinate dependent “axion”

Suppose the theory of fermions interacting with EM field and the axial 4-vector $b_{\mu}$: $$ S = \int d^{4}x \bar{\psi}\gamma^{\mu}(i\partial_{\mu} + eA_{\mu} +\gamma_{5}b_{\mu})\psi $$ We want to ...
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1answer
129 views

Chemical potential in 1D

How is it possible to understand how the chemical potential $\mu$ of the electrons in the Sommerfeld theory of metals change, when the temperature $T$ is increased up to a small value above zero? By ...
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1answer
2k views

Fermi-Dirac distribution in the high-temperature limit

I am reading "Electronic Transport in Mesoscopic Systems" by Supriyo Datta and am a little confused by his discussion of the Fermi Dirac distribution function, which is given by: $$f(E)=\frac{1}{\...
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1answer
60 views

Breaking down sawdust pellets causing heat

We just discovered that pellets (sawdust, animal feed, organic constituents) when re-hydrated give off heat. We understand this at molecular levels but are having a hard time sussing this out at a ...
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1answer
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How does the number of excited fermions and holes affect the chemical potential?

Given we know the number of states filled with excited fermions with positive energy and the number of non-filled states with negative energy, what relation does the chemical potential have to that? ...