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.
Does fermi level (in metals) depend on the density of states? I am asking this because from fermi-dirac distribution it seems like that fermi level is non-dependent of DOS, but there is chemical potential in fermi-dirac distribution, which is said to be dependent of DOS.
So I think I have the principles mixed up here because I'm getting kind of "circular" answers.
## N = N_1 + N_2##
##dN## = 0 bc/ particle number fixed so ##dN_1 = -dN_2##
##F = cN^2 = c(N_1 + N_2)^2##
In diffusive equilibrium, free energy would be minimized and chemical potentials equal...
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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...
Greetings,
I realized that I don't understand a fundamental fact of common Li-ion batteries.
During the charging process, electrons are forcefully extracted from the cathode and pushed into the anode. Charge balance then yields a flow of positive Li ions from the cathode to the anode (through...
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...
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...
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...
Ignoring cross-diffusion, diffusive mass fluxes down chemical potential gradients can be described by the equation (I am working from de Groot and Mazur's 1984 text on non-equilibrium thermodynamics):
\frac{\partial C_k}{\partial t} = L_{kk}\frac{\partial (\mu_k-\mu_n)}{\partial x}
where C_k...
Homework Statement
Suppose you are given the following relation among the entropy S, volume V , internal energy U, and number of particles N of a thermodynamic system, where A is a constant.:
$$ S = A(NVU)^{\frac 1 3} $$
Find the chemical potential μ(T,P)
Homework Equations
$$ \frac μ T =...
When determining the formation energy associated with a point vacancy in say a monoatomic crystal - when the total energies of both perfect and defected crystals are known - how exactly is the chemical potential determined?
Formation Energy should be given by expression...
Homework Statement
(Excerpted from a longer, multipart problem but essentially)
Show that for an ideal gas,
$$ \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...
Homework Statement
Derive an equation for the change in free energy, ΔGmixing, when ideal gases with the same temperature and pressure, are mixed.
Homework Equations
ΔGmixing = nRT∑(xi)ln(xi)
(∂/∂T(G/T))p = -H/(TxT)
The Attempt at a Solution
Pi = xiPi*
μi = Gi,m
μ = (∂G/∂n) at constant T...
Homework Statement
Consider a monatomic ideal gas that lives at a height z above sea level, so each molecule has potential energy mgz in addition to its kinetic energy.
(a) Show that the chemical potential is the same as if the gas were at sea level, plus an additional term mgz:
μ(z) =...