Questions tagged [chemical-potential]

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.

Chemical Potential in thermodynamics is defined by $$\mathrm{d}U= T\mathrm{d}S - P\mathrm{d}V + \sum_{i=1}^n \mu_i \,\mathrm{d}N_i$$ where $U$ is the Internal Energy of the system; $S$ is the Entropy of the system; $N$ is the Number of Particles in the system; $V$ is the Volume of the system; $P$ is the systems' Pressure; $T$ is the absolute (thermodynamic) temperature of the system and $\mu$ is the Chemical Potential of the system.

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Can a radioactive atom be prevented from decaying if it's in a REALLY strong chemical bond?

So, based on this question, a molecule containing a radioactive atom will break when the atom decays. But suppose you need a lot energy to break the compound apart --- as in, more energy than the decay of the atom will release (obviously, a molecule…
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What's the difference between Fermi Energy and Fermi Level?

I'm a bit confused about the difference between these two concepts. According to Wikipedia the Fermi energy and Fermi level are closely related concepts. From my understanding, the Fermi energy is the highest occupied energy level of a system in…
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Chemical potential

This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at hand where the chemical potential is negative.…
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Meaning of the chemical potential for a boson gas

My lecturer told me that $\mu$, the Chemical potential, is zero or negative, and in the following example, mathematically it acts as a normalization constant. But is there any physical insight about why boson gas can be zero or negative? I think it…
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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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Why is the chemical potential of a photon gas 0 (mathematical argument)?

$$dU=TdS-PdV+\mu d\bar{N}$$ $$\mu=\left(\frac{\partial U}{\partial \bar{N}}\right)_{S,V}$$ The energy of each photon is given by $\hbar\omega$ (each photon obviously carries energy). Therefore the addition of a photon to a photon gas must increase…
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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 what we really mean by voltage drop). However, I have…
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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 obtained from number non-conservation?
richard
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How can $\mu$ be nonzero if grand canonical density operator commutes with $\hat{H}$?

In the grand canonical ensemble, the equilibrium density operator is given by $$\hat{\rho}_{\rm eq}=\frac{1}{Z}e^{-\beta\left(\hat{H}-\mu\hat{N}\right)}, ~{\rm with}~ Z={\rm tr}\left[e^{-\beta\left(\hat{H}-\mu\hat{N}\right)}\right].$$ Here,…
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How do you measure the chemical potential?

It is clear how to measure thermodynamics quantities such as temperature, pressure, energy, particle number and volume. But I have no idea how to measure chemical potential. Could someone please provide some examples of how one could measure the…
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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 $\Phi=A_t(r=\infty)$ at the boundary of the bulk such that…
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How do you experimentally measure the chemical potential of a gas?

How does one measure the chemical potential of a substance/ thermodynamic system? I am asking this question for two reasons: (1) The measure on phase space: Textbooks typically state that one should take the integral measure on phase space to be…
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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, 321(5–6):381 – 387, 2004. one cannot have the…
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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: $$f(E)=\frac{1}{\exp\left[\frac{E-E_f}{k_BT}\right]+1},$$ where $E$…
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Fermi level and conductivity

Can someone in a simple way explain me what the Fermi level is and what does it have to do with conductivity. My teacher said that Cu conducts electric current better than Al because of something in relation to Fermi level, I didn't get him very…
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