# Tagged Questions

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### Can I calculate all mass fractions given all chemical potentials?

I am considering a closed, adiabatic, isobaric perfectly-stirred reactor. I'm also assuming that the contents are ideal gases, i.e. that $$\mu_\alpha = \mu^{\circ}_\alpha + R T \ln P_\alpha$$ I ...
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### Total chemical potential of electrons in pn junction

I am reading this page about electron energy concept terminology. I am trying to apply that for the pn junction in equilibrium below. Could anyone help me to see if I get it correctly? C = ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 r)...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 there ...
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### 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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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 average"...
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### 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 ...