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9
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3answers
354 views

Is particle number a problem for formulating statistical physics in a mathematically rigorous manner?

Quantities like the chemical potential can be expressed as something like $$\mu=-T\left(\tfrac{\partial S}{\partial N}\right)_{E,V}.$$ Now the entropy is the log some volume, which depends on the ...
9
votes
2answers
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 ...
7
votes
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 ...
7
votes
2answers
494 views

How much Bicarbonate of Soda and Vinegar would I need to reach space?

So here is my problem - as part of my job I present some science demonstrations to children and one of the tricks I regularly use is the bicarb/acetic acid rocket. I thought the other day that a ...
7
votes
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 ...
6
votes
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 ...
6
votes
2answers
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 ...
6
votes
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 ...
6
votes
1answer
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 ...
5
votes
4answers
2k views

Chemical potential of a Bose gas

In my course, there is this fact : In a Bose gas, the chemical potential $\mu$ must always be lower than the smaller level of energy $\epsilon_0$. I find this strange, because if we put a Bose ...
5
votes
2answers
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 ...
4
votes
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 ...
4
votes
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: ...
4
votes
1answer
929 views

Energy per particle vs. chemical potential vs. evaporation energy

There is a system of N particles. They interact and are bound together with a binding energy Eb (or potential energy). To characterize the system there are multiple terms Energy per particle Eb(N)/N ...
4
votes
1answer
402 views

Voltage drop over a cell membrane

Again, a problem from exam preparation: [A] cell's membrane allows sodium ions to pass through it, but not chlorine ions. The cell is placed in a salty solution with a ten times higher ...
4
votes
0answers
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 ...
3
votes
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 ...
3
votes
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 ...
3
votes
1answer
2k views

What does activation energy actually do?

Spontaneous (exothermic) chemical reactions often require a push from the addition of externally supplied energy. This energy is often called activation energy. What does activation energy actually ...
3
votes
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 ...
3
votes
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 ...
3
votes
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 ...
3
votes
1answer
463 views

Why do hydrogen atoms attract?

That is, why is the potential energy with the orbitals overlapping less than with the Hydrogen atoms 'independent'. Similarly, why is a noble gas configuration stabler than if an electron were to be ...
3
votes
1answer
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 ...
2
votes
1answer
575 views

Internal Energy and entropy in a open system

Here http://en.wikipedia.org/wiki/Internal_energy we can read $$U= TS-PV+\sum_i \mu_i N_i$$ Let's suppose i=1 and a ideal gas. We know: $$U=N/N_A c_v T$$; $$PV=NKT$$; $$\mu=\frac{\partial ...
2
votes
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 ...
2
votes
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 ...
2
votes
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 ...
2
votes
2answers
111 views

Ashcroft Mermin Eq. 17.47ff

In "Solid State Physics" by said authors, Eq. 17.46 is $$ \rho^{ind}(\textbf{r}) = - e[n_0(\mu + e\phi(\textbf{r})) - n_0(\mu)]$$ and then the authors write In the present case we assume that ...
2
votes
1answer
416 views

How does the internuclear repulsion vary in Hydrogenic atom collision?

Hydrogen fusion requires two hydrogen nuclei to get close enough (typically a few fm) to fuse. Much of the problem of creating a fusion reactor is overcoming the Coulomb repulsion between a pair of ...
2
votes
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 ...
2
votes
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 ...
2
votes
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 ...
2
votes
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 ...
2
votes
1answer
1k views

Calculating the derivative of the average number of particles by the chemical potential

This should be a trivial calculation but somehow I have managed to get myself confused about this. The grand partition function is: $\mathcal Z = \sum_{N=1}^\infty \sum_{r(N)} {\text e}^{-\beta E_r ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
1
vote
3answers
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. ...
1
vote
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 ...
1
vote
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 ...
1
vote
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 ...
1
vote
2answers
2k views

What is the physical or mathematical meaning of the Gibbs-Duhem equation?

The Gibbs-Duhem equation states $$0~=~SdT-VdP+\sum(N_i d\mu_i),$$ where $\mu$ is the chemical potential. Does it have any mathematical (about intensive parameters) or physical meaning?
1
vote
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 ...
1
vote
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 ...
1
vote
0answers
23 views

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 ...
1
vote
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 ...
1
vote
0answers
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 ...
1
vote
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} ...
1
vote
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 ...
0
votes
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 ...