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8
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2answers
551 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
3answers
306 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 ...
7
votes
2answers
385 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
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0answers
59 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 ...
4
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3answers
845 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 ...
4
votes
1answer
693 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
268 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 ...
3
votes
1answer
80 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 ...
3
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1answer
147 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
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1answer
891 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
1answer
162 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: ...
3
votes
1answer
787 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
287 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 ...
2
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1answer
518 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
2answers
37 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
124 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
104 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
309 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
69 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
156 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
851 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 ...
1
vote
3answers
2k 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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2answers
53 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
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1answer
158 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
2answers
1k 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
58 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
307 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 ...
0
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1answer
183 views

Ways to experimentally control the chemical potential of a solid state system

When working in the grand canonical ensemble we write the grand potential as $\Omega = \Omega (T,V,\mu)$. In this case we are taking the chemical potential $\mu$ to be an independent variable. This ...
0
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0answers
11 views

What's the difference between electrostatic potential and electrochemical potential along a (semi)conductor?

According to wikipedia: the electrochemical potential, $\bar{\mu}$, sometimes abbreviated to ECP, is a thermodynamic measure of chemical potential that does not omit the energy contribution of ...
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0answers
53 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 ...
0
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3answers
6k views

How does evaporation affect the temperature of the air?

A wet object or a volume of water will decrease in temperature due to the effect of evaporation. We understand this to be because of the molecular kinetics, where the faster water molecules escape ...