Chemical potential Definition and 97 Threads

In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species in a mixture is defined as the rate of change of free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are added to the system. Thus, it is the partial derivative of the free energy with respect to the amount of the species, all other species' concentrations in the mixture remaining constant. The molar chemical potential is also known as partial molar free energy. When both temperature and pressure are held constant, chemical potential is the partial molar Gibbs free energy. At chemical equilibrium or in phase equilibrium the total sum of the product of chemical potentials and stoichiometric coefficients is zero, as the free energy is at a minimum.In semiconductor physics, the chemical potential of a system of electrons at zero absolute temperature is known as the Fermi energy.

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  1. M

    I Minimization of the Gibbs energy when number of molecules varies

    I have a rather basic question regarding the chemical potential (##\mu##) in thermodynamics and its relation to the Gibbs free energy (##G##). All thermodynamics textbooks I've looked at (Landau & Lifshitz, Kittel...) derive the fact that, at constant temperature ##T## and pressure ##p##, the...
  2. E

    I How to see this form for the chemical potential of an ideal gas?

    In Chapter 13.2 of his text, Callen states that the chemical potential with respect to the ##j##th component of an ideal gas can be written as $$\mu_j = RT \left[\phi_j(T) + \ln P + \ln x_j \right].$$ He states this outright and doesn't prove it, and I am trying to do so now. Based on what has...
  3. Dario56

    Concept of Absolute Thermodynamic Activity

    In the textbook Electrochemical Systems by Newman and Alyea, Chapter 14: The definition of some thermodynamic functions, chemical potential of component (ionic or neutral) is written as a function of absolute activity: $$\mu_i=RT\ln(\lambda_i)\tag1$$ where ##\lambda_i## is the absolute activity...
  4. G

    Calculating Chemical Potential from Energy Derivatives

    Hi Unfortunately, I can't get on with the following task. The system looks like this it is divided in such a way that the same number of particles is present in each ##\epsilon## section. I am now to determine the energy ##E(P_h,V_h,N)## at the height h using the energy ##h=0## i.e...
  5. chikchok

    I Chemical potential and Fermi level

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  6. B

    Calculating particle numbers in diffusive equilibrium of a battery

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  7. Kaguro

    Chemical potential and fugacity

    I am trying to learn statistical physics. While learning MB statistics, my textbook defined chemical potential as ##\mu = (\frac{\partial F}{\partial N})_{V,T}##. That's nice. Later when I started on Quantum statistics, my textbook described all three distribution functions via: ##n_i =...
  8. J

    Thermodynamics problem relating to Chemical Potentials

    For part (a), I used this formula where where the i's represent the substance being used and mu_i^0 represents some reference potential. However, to my knowledge this simply calculates the change in chemical potential from one state to another which is not of much help in finding the relative...
  9. E

    Meaning of small triangle in chemical potential

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  10. QuarkDecay

    B Chemical Potential μ in Solids

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  11. cahill

    I Change in chemical potential energy from nuclear decay

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  12. SchroedingersLion

    Batteries: Is the current a diffusion current?

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  13. W

    Thermal Physics: Fermi Gas and chemical potential

    Hi all, I have an issue trying to understand the following paragraph from Blundell's book. How, exactly, does the definition of ##\mu_0 = E_F## "make sense"? In the sentence after 30.21, it seems to say that the mean energy for a system with ##N## particles differs from that of a system with...
  14. L

    I What is the relation between chemical potential and the number of particles?

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  15. steroidjunkie

    Semiconductor chemical potential and the density of holes

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  16. P

    I Chemical potential on a solid and its vapor pressure

    I have been reading the book "Nanostructures and Nanomaterials" by G. Cao and Y. Yang, and was intrigued by the following passage in page 33: "Assuming the vapor of solid phase obeys the ideal gas law, for the flat surface one can easily arrive at: μv − μ∞ = −kTlnP∞, where μv is the chemical...
  17. amjad-sh

    A What is the significance of spin chemical potential in physics?

    Can somebody give me some insights related to spin chemical potential ? I searched on google but didn't get satisfied. What it means when two spin groups of electrons (group A with spin up and group B with spin down)have different spin chemical potential?
  18. Pushoam

    Relation between chemical potential and S,V,T,P

    Homework Statement Homework EquationsThe Attempt at a SolutionChemical potential is defined as ## \mu = Gibbs potential per particle ##. So, is the system consists of N particles, ##\mu = \frac { G } {N } ##. Now, dG = VdP – SdT ## \frac {dG } { N } = \frac { VdP } { N } - \frac { SdT }...
  19. F

    Standard chemical potential and activity of asphaltene

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  20. V

    B Can Fermions Exhibit Negative Chemical Potential Like Bosons?

    Is possible and what does it mean if a chemical potential is negative? I mean that for boson it means that in environment is "needed" boson (photon) and is possible to create him. Is it true? And what about for fermions? Could it mean that it is pleasent for environment to creat some fermion? Or...
  21. W

    Thermodynamic Identity: Chemical Potential

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  22. M

    Chemical potential using Boltzmann equation

    Homework Statement I must calculate chemical potential using the Boltzmann equation in relaxation time approximation $$f=f^0-\tau v_z^2 \partial f^0/\partial z,$$ where ##f^0## is given as $$f^0 = 2(\frac{m}{2\pi\hbar})^3 \frac{1}{\exp{\beta(z)(\frac{mv^2}{2}-\mu(z))}+1}$$ I have to consider...
  23. RicardoMP

    I Sommerfeld Expansion & Chemical Potential

    Hi! I'm trying to show how the chemical potential depends on the temperature and I'm advised to use the Sommerfeld expansion. I'm using it on the density of charge n=\int^{+\infty}_{-\infty} \rho(\epsilon)n_Fd\epsilon , which gives n=\int^{\mu}_{0} \rho(\epsilon)d\epsilon...
  24. D

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  25. H

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  26. Mayan Fung

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  27. L

    Chemical potential at equlibrium

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  28. M

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    When determining the formation energy associated with a point vacancy in say a monoatomic crystal - when the total energies of both perfect and defected crystals are known - how exactly is the chemical potential determined? Formation Energy should be given by expression...
  29. Einj

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  30. Crush1986

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  31. Coffee_

    How is the chemical potential defined when keeping entropy and volume constant?

    The chemical potential is defined as ##µ=\frac{\partial E}{\partial N}## while keeping entropy and volume constant. Well how to keep the volume constant while adding particles is obvious but what about the entropy? Obviously adding a particle at a certain energy ##E_{p}## changes the total...
  32. C

    Chemical potential equilibrium cosmology

    In Dodelson's "Introduction to Modern Cosmology" at p. 61 he introduces a non- equilibrium number density $$n_i = g_i e^{\mu_i/T} \int \frac{d^3p}{(2\pi)^3} e^{-E_i/T}$$ and an equilibrium number density $$n_i^{(0)} = g_i \int \frac{d^3p}{(2\pi)^3} e^{-E_i/T},$$ from which it follows that the...
  33. It's me

    Chemical potential of water using the Van der Waals model

    Homework Statement Obtain the chemical potential of water as a function of temperature and volume using the Van der Waals model. Homework Equations μ=∂U∂N The Attempt at a Solution I don't really understand how to do this at all. Any help would be greatly appreciated.
  34. A

    Chemical Potential: Pressure, Fugacity, & More

    Chemical potentials can be written with an an ln term which has pressure, fugacity, concentration, activity coeff times concentration, mole fraction, and mole fraction times activity coeff. Is there any source that makes sense of this?
  35. T

    Relationship between pressure & chem potential in ideal gas

    Homework Statement (Excerpted from a longer, multipart problem but essentially) Show that for an ideal gas, $$ \frac{\partial p}{\partial T}\bigg)_\mu = \frac{S}{V}. $$ Homework Equations • The ideal gas law, of course $$ pV = Nk_{\rm B}T $$ • Pressure, temperature, and chemical potential...
  36. L

    Thermodynamics: ideal gas chemical potential

    Can someone explain me why we could put pi, μi and μiο in this equation: and we get this: (this is The chemical potential of a component in a perfect mixture of ideal gases wher pi is partial pressure)
  37. ChristineMarie

    Molar Free Energy of an Ideal Gas at Temperature T and Pressure P

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  38. D

    How Do You Find Internal Energy with Chemical Potential?

    Homework Statement Given dE=TdS-PdV+\mu dN, PV=NT and Cv=\frac{3}{2}N Find E Homework Equations dE=TdS-PdV+\mu dN, PV=NT and Cv=\frac{3}{2}N The Attempt at a Solution That part that is confusing me is the chemical potential, not sure what to do with it. Finding the energy for the ideal...
  39. B

    How is Chemical Potential Affected by Altitude in an Ideal Gas?

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  40. C

    Why is the chemical potential negligible at equilibrium?

    I am currently reading cosmology and I read the statement "... chemical potential which is nearly always negligible when processes are in equilibrium." So the current understanding I got of chemical potential is through the law: $$dE = - pdV + TdS + \mu dN.$$ Hence for processes which occur at...
  41. alpha358

    Thermodynamics: ideal gas chemical potential pressure dependence

    I don‘t understand one step in derivation of ideal gas chemical potential. Generally Gibbs free energy is: (1) (2) We observe that: (3) From equation (3) we make differential equation and integrate it: (4) (5) We get Gibbs free energy dependence on pressure...
  42. A

    Crystal Lattice of Spin-1 Particles: Chemical Potential?

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  43. D

    Chemical potential for van de Waarls gas

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  44. Useful nucleus

    Bounds on the chemical potential of electrons

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  45. A

    Entropy, chemical potential, temperature

    For a thermodynamic system there exists a function called entropy S(U,N,V) etc. We then define for instance temperature as: 1/T = ∂S/∂U μ = ∂S/∂N etc. When taking these partial it is understood that we only take the derivative of S wrt the explicit dependece on U,N etc. right? Because...
  46. A

    Half-Filled Band: Explaining Zero Chemical Potential

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  47. A

    Are Temperature and Chemical Potential Independent in Current Flow Models?

    I have seen various treatments of the chemical potential. Basically it all amounted to a definition of it as a quantity maximizing the entropy for systems allowed to exchange particles. Now this quantity has become quite important in some models I am studying for current flow, specifically an...
  48. T

    How is Work Calculated from Chemical Potential and ΔG in a Two-Chamber System?

    Homework Statement Consider a container with two chambers of the same size separated by a fixed membrane in the middle (permeable only to the ideal solute, but not the solvent). One chamber initially contains 1M of solute, and the other contains 0.5M of solute. Write an equation for the...
  49. I

    Chemical Potential: Heat Energy Carried by Particles

    in class, we just learned that the chemical potential was μ=∂G/∂N i'm looking in my book and it says that μ=-T(∂S/∂N) this looks a lot like the partial of heat energy with respect to N. is my interpretation correct? (assuming my interpretation was correct): so qualitatively, the...
  50. G

    Why particles flow from high chemical potential to low

    Homework Statement Why does the equation (d2G/dNi2)T,P=(dμ/dNi)T,P>0 tells you that particles will flow from high chemical potential to region of low chemical potential at const. temperature and pressure? Thank you all. Homework Equations dG=VdP-SdT+μdNi The Attempt at a Solution...
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