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Temperature dependent chemical potential

Chemical potential is determined by the number of electrons in the system and coincides with the Fermi energy at zero temperature. The chemical potential can shift as temperature changes if the ...
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1answer
78 views

Intuition about the cosmological significance of the chemical potential

A definition of the chemical potential that has always served me well is $$\mu_i = \Big(\frac{\partial U}{\partial N_i}\Big)_{S,V},$$ that is, the amount of energy one would have to add to a system ...
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Explanation of chemical potential

I made a NVT Lennard Jones Monte Carlo simulation. In this simulation I calculate the chemical potential of my system with $$\mu = \mu_{id} + \mu_{ex} $$ Where $\mu_{id}$ is the chemical potential of ...
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1answer
16 views

how does voltage sensitive dye determine the membrane potential?

There are so many papers about VSDs and how to use them, but i can not find anything about what exactly is happening in the cell membrane that leads to the change in VSD's light intensity as a sign of ...
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34 views

What happens when a semipermeable membrane allows only one solute to pass through?

I'm essentially a medical student where we deal a lot with osmosis. But when we are taught, it is done generally with only a single solute in consideration. What if two different solutes are used on ...
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1answer
63 views

Chemical Potential in the canonical and grand canonical ensemble

I'm studying the ideal Fermi gas from "Statistical Mechanics", by R. K. Pathria. In particular, the following formula, which can be found on page 237: \begin{equation} \mu=\left(\frac{3N}{4 \pi g ...
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1answer
17 views

Galvanic cell of zinc half cell and copper half cell

Where do the $Zn^{+2}$ ions come from in a $Zn$-half cell, if from zinc metal then why doesn't after some time $Zn$ metal is completely vanished and what is the purpose of $Zn^{+2}$ ions of zinc ...
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2answers
107 views

Why does the chemical potential vanish for Bose Einstein condensate?

the reasoning in a Bose Einstein condensate is to try to account for all the particles in the excited continuum states by tuning the chemical potential. However at a critical temperature $T_c$ the ...
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22 views

Gibbs isotherm and calculating interfacial tension change from first principles

Question: Is it possible for a solid particle to change the surface tension between two phases? (or: Does a solid particle have a chemical potential?) This question stems from the more ...
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70 views

Physical interpretation of the chemical potential in Bose and Fermionic gas

I understand that both Fermions and bosons have the chemical potential $\nu <0$ when it is T>0, but still behave classically, the fermions would increase its chemical potential at T=0, whereas the ...
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74 views

Is there a tool to measure the chemical potential of a system?

Let's suppose I put you inside a room filled with a gas. You can measure its pressure directly with a barometer. You can measure its temperature directly with a thermometer. Can you measure its ...
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38 views

Extra 5/2 tau term in chemical potential of a monoatomic ideal gas? [closed]

The chemical potential of an ideal monoatomic gas should be: $\mu = \tau ln \frac {n}{n_Q}$ http://web.mit.edu/ndhillon/www/Teaching/Physics/bookse5.html I get this result if I derive it using the ...
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1answer
48 views

why is the chemical potential included in the hamiltonian for a systeme coupeled to a particle reservoir

I am beginning with second quantification language so i saw that if we are in grand canonical ensemble then: $$ H=H_0 - \mu N $$ naturally i thought that this $ \mu $ would be included in the ...
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2answers
188 views

Why is chemical potential, μ=0 when calculating critical temperature of BECs?

How do we justify taking the chemical potential, $\mu$ as $0$ when calculating the critical temperature of Bose-Einstein Condensates (BECs)? I apologise as I do not how to use LaTeX, for if I did the ...
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1answer
52 views

Sign conventions in Hubbard model

The Hubbard model is often expressed as $$H=-J\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} ...
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272 views

Physic explanation to osmosis

I want to understand the forces involved in osmosis. If I have a molecule of water and one of a salt in the left side of a semi-permeable membrane, and a water molecule at the right side, what forces ...
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1answer
59 views

Is kinetic energy related to chemical potential?

I wonder if the kinetic energy written as $\frac{d\mathbf x}{dt}\cdot d\mathbf p$ is related to chemical potential? I ask because if I use $\mathbf p = m \frac{d\mathbf x}{dt}$ as a constitutive ...
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1answer
435 views

Fermi Level: chemical potential vs. electrochemical potential

In solid-state physics it is understood that the Fermi-Level is the electrochemical potential. The Fermi-Level is defined to: However, in thermodynamics this formula is referred to as the ...
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1answer
81 views

Under what conditions is air is in chemical equilibrium?

I am considering the flow field around a hypersonic glide vehicle at $M=7$. As I understand it, air is in chemical equilibrium if the fluid time scale $t_f \ll t_c$, where $t_c$ is the chemical time ...
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146 views

How to compute this change of Gibbs energy for a Van der Waals gas?

The change of Gibbs energy at constant temperature and species numbers, $\Delta G$, is given by an integral $\int_{p_1}^{p_2}V\,{\mathrm d}p$. For the ideal gas law $$p\,V=n\,RT,$$ this comes down to ...
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1answer
57 views

What's the difference between the Fermi level and the electrochemical potential?

I was asked in a Thermostatistics test to compute the electrochemical potential $\mu(T)$ and the Fermi level $\epsilon_F$ for a system of non-interacting fermions, with two possible energetic states ...
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1answer
171 views

What does chemical potential $\mu = 0$ mean?

First off, just to be clear, the chemical potential being equal to zero is different from not having a chemical potential at all (e.g. a photon gas)? Now: physically, what does having chemical ...
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15 views

how to show that the chemical potential goes with O(1/V)?

In statistical mechanics books $\mu=O\left(\frac{1}{V}\right)$ is being used to show the nature of the chemical potential when $T\to0$ Unfortunately, I was not able to figure out how to see how this ...
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1answer
84 views

Understanding chemical potential in AdS/CFT

I always find it very difficult to understand the notion of chemical potential physically/intuitively unlike pressure and temperature in statistical mechanics. Can some one suggest some nice ...
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1answer
123 views

Work and chemical energy “paradox”

This is a mistake I've seen many people make, a few physicists included, but I haven't ever seen a satisfactory explanation for what's going on. Apologies for the lengthy setup. Setup Suppose I ...
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94 views

Why $\epsilon > \mu$ for Bose-Einstein distribution (but not for Fermi-Dirac)?

For fermions $$\bar{n}_{FD}=\frac{1}{e^{(\epsilon -\mu)/kT}+1}$$ and $\epsilon$ can be bigger or small than $\mu$. However, for bosons: $$\bar{n}_{BE}=\frac{1}{e^{(\epsilon -\mu)/kT}-1}$$ which ...
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21 views

Effect of applying a gate voltage to a strongly correlated system

In strongly correlated systems, there are different ways of driving a metal-insulator transition (MIT), say, bandwidth control, filling control and dimensionality control (See MIT). As for the method ...
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1answer
227 views

Chemical Potential as a function of Temperature

I have considered an ideal fermi gas. Then, we can obtain an expression for chemical potential as a function of Temperature. I want to understand the physical significance to it or what it really ...
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1answer
73 views

How to thermodynamically understand process of burning a piece of coal?

Let's imagine that I have a match in hand and nugget of coal on my desk. Then I light up the match and place it for few seconds near the coal so a tiny piece of nugget catches fire. Then another piece ...
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194 views

Confusing Chemical potential of mixtures

I feel that there are very few textbook that treat the chemical potential of mixtures in an understandable clear way, which is why I wanted to ask here about certain things? Although I do not have a ...
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1answer
138 views

Chemical Potential, Boltzmann

The electrochemical potential of an ion i in an electrolytic solvent is given by: \begin{align}\mu_i(\vec r) &= \mu_i^0 + RT \ln(a_i(\vec r))\\& = \mu_i^0 + RT \ln(\gamma_i(\vec r) c_i(\vec ...
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777 views

If we connect a long wire to a battery, will battery produce more electrons?

I actually have three related questions: An open circuit chemical cell separates charges creating a surplus of electrons on its negative terminus and a shortage of electrons on its positive terminus. ...
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336 views

Diffusion in a chemical potential gradient

I am having troubles to understand to connection between equilibrium and non equilibrium thermodynamics. I am studying a mixture of molecules $A,B,C$ and solvent $S$. The free energy $F$ is given by ...
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1answer
65 views

Equivalence of different definitions for chemical potential

In some books, the chemical potential is defined in term of the Gibbs energy as $$ \mu_i \equiv \left( \frac{\partial G}{\partial n_i} \right)_{P,T,n_j} $$ where $n_j$ indicates all mole numbers ...
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2answers
77 views

Energy Flux due to Diffusion

Per the Fundamental Thermodynamic Relation, I know that the chemical potential of $i$ represents the energy which would added to a system if a particle of $i$ were added with all other system ...
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2answers
142 views

Ambiguity on the notion of potential in electrical circuits?

As everybody else I have been taught elementary electrical circuits from secondary school to engineering level in analog electronics at university. Invariably, the notion of potential used to ...
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1answer
86 views

Chemical potentials for multicomponent solids

I have a problem understanding how to deal with the chemical potential when two thermodynamic systems are in contact. For simplicity, let us consider $T=0\ K$. We have a system that is composed of two ...
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2answers
127 views

If batteries are a source of energy, would not lower-valued resistors cause a violation of the conservation of energy?

Here's the conundrum I have been facing. Yesterday I asked the question: how can batteries constantly motivate electrons to complete a circuit? (What maintains constant voltage in a battery?) After ...
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1answer
908 views

What maintains constant voltage in a battery?

I know there's lots of questions that address similar situations, (Batteries connected in Parallel, Batteries and fields?, Naive Question About Batteries, and the oft-viewed I don't understand ...
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1answer
204 views

Role of the canonical ensemble and electric charge in AdS/CFT

If we consider a charged black hole in AdS spacetime, we can either do thermodynamics in the grand canonical or the canonical ensemble. In the former, we fix the electrostatic potential ...
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81 views

Proving $RTln(a_i)$ equal to non PV work done by system,where $a_i$ is activity

First of all many here will might say that it is Chemistry question.If you think so then read this article and then answer question. Question is --- We know chemical potential is defined as $\mu_i ...
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1answer
1k views

Chemical potential of Bose-Einstein condensation

This is a problem in An Introduction to Thermal Physics. (a)(b) is easy to work out. In (c), I use the formula $N_{excited}=(\frac{T}{T_c})^{3/2}N, \ (T<T_c)$ to calculate how many atoms are ...
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1answer
305 views

Difference in chemical potential in supersaturated solutions

I have been more or less struggeling to understand an equation that is apparently used in almost all books covering crystals in any way. Basically every book that I have found explains the following: ...
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1answer
219 views

Questions about Statistical Mechanics

For grand partition ensemble, is it true that the introduction of chemical potential allows us to have the sum of number of the particles in each state to be the total number of particles ("On ...
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4answers
7k views

Meaning of the chemical potential for a boson gas

My lecturer told me that the mu is the Chemical potential is zero or negative, in the following example, mathematically it acts as a Normalisation constant. But is there any Physical insight about why ...
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1answer
264 views

Does non-conservation of number of particles imply zero chemical potential?

In the systems like photon gas in a cavity and phonon gas in a solid number of particles is not conserved and chamical potential is zero. Is this a general rule? If yes, how zero chemical potential is ...
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1answer
302 views

Vortices and chemical potential in topological superconductors

I am trying to read up some review articles about Majorana physics in topological material, but I am not really familiar with the condensed matter terminology (with condensed matter in general I ...
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1answer
2k views

Diffusion of gas in a liquid with changing pressure and solubility (chemical potential)

Modelling the diffusion of a gas dissolved in water in a vertical column of water, several meters deep. Also assuming the water is completely still, so only diffusion plays a role. (Actually a model ...
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1answer
280 views

Mathematical form of chemical potential difference and entropy production

I'm trying to understand the form of the 'force' which drives chemical reactions, ie. the difference in chemical potential, also sometimes called the 'affinity'. $$\Delta \mu = - kT ln ...
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1k views

Could the chemical potential of a Bose gas be zero?

Could the chemical potential of a Bose gas be zero ? If it was the case, we will have an infinite number of particles in the ground state ! No ? But I've heard that for $T < T_c$, $\mu = 0$, so I ...