Chemical potential Definition and 97 Threads

So the expression for Gibb's free energy is: dG = -SdT + VdP + μdN, Here, we see that the Gibb's free energy changes with temperature (dT), change in pressure (dP) and change in chemical potential (as a result of change in particle number). My question is: we know chemical potential...

So when osmosis between two solutions (separated by a semipermeable membrane),takes place, the solvent travels from the side where its chemical potential is higher to the side where its chemical potential is lower. However, this results in a difference of levels of fluids across the membrane...

Can we talk about the chemical potential of a system with fixed number of particles? Is this physically meaningful? Why/why not? P.s: I know that chemical potential is the partial derivative of free energy with respect to number of particles. But in the formulation of grand canonical...

I have a quick question, is the chemical potential $$\mu=\partial F /\partial N$$ where F is the free energy physically equivalent to a potential or energy? For example, in electrostatics, $$V=U/q$$ Does $$\mu_{ext}= U \text{ or } V$$ Also, same thing could be asked about gravity...

What is the formula used to find out the chemical potential of a molecule or atom?

Homework Statement The latent heat of vaporization of a substance is defined as the amount of heat required to transform the substance from its liquid into its vapor phase. A certain material has a boiling point of 700K and its molecules have three degrees of freedom in the liquid phase but...

It is probably a silly question, but here it is. Suppose we have a gas composed by two different kinds of particles. There will be two different kinds of chemical potential? One for each specie?

Homework Statement Basically, find the chemical potential of an ideal gas knowing its heat capacities.Homework Equations P V = n R T \ \ \ \ (1) U = n c_V T + U_0 \ \ \ \ (2) S = S_0 + n c_V ln (T) + nR ln (V) = S_0 + n c_V ln (T) + nR ln \left ( \frac{nRT}{P} \right ) \ \ \ \ (3) \mu = \left...

Homework Statement I am working Problem 5.29 *** (b) in Griffiths QM. We are asked to show that m(T) monotonically increases as T decreases, assuming N and V are constants. m(T) - is chemical potential. Homework Equations Too many to list, probably easier to look in the book if you...

For any system where the thermodynamic limit exists, we know that the internal energy U, the entropy σ, the total particle number N and the total volume V are all extensive. Because of this, we know that the Euler relation holds true U = -PV + \tauσ + \muN and that the chemical potential...

hi, can someone help me in understanding the difference between chemical potential and activity? Why it is important to know/determine activities of certain species in material growth? Given that activity is dimensionless quantity, what is it measuring? Also, what is the activity of pure...

Doing some fun problems in Keith Stowe's 'An Introduction to Thermodynamics and Statistical Mechanics'. Good book. Problem statement: A certain material vaporizes from the liquid phase at 700 K. In both phases, the molecules have three degrees of freedom. If u_{0} in the liquid phase is...

μ/T represents the change in entropy if we change the number of particles,, so according to the fundamental assumption of statistical mechanics μ/T should tell us about the tendency of two systems to exchange particles... but I am having a hard time imagining how rotational or vibrational...

How can I measure the chemical potential of a gas (not necessarily ideal), using calorimetry alone? I mean, without knowing any equations of state, being able to measure pressure, temperature, volume, and number of particles. Also, I can add a measured amount of heat energy to the gas using a...

Hi all, In the solid state physics course I took a year ago we used the chemical potential μ which appeared inside the fermi-dirac distribution function to describe the energy that above it no electrons resides and below it they all reside as the temperature reaches 0 kelvin. Now, when I...

Homework Statement Find the chemical potential for an ideal gas as a function of temperature and pressure. Use the "Gibbs-Duhen relation". Homework Equations \mu=\frac{\partial U}{\partial N} dU=TdS-pdV+\sum\limits_{i}\mu_{i}dN_{i} U=Q+W Gibbs-Duhen relation...

hi there first excuse me for my poor english! can anyone explane what the hell is the 'saturation chemical potential'?! and how can i get it? thanks guys

Hello everyone, first post here. In trying to decipher the meaning of chemical potential, I feel as if at least in the context of the Fermi-Dirac Distribution I have almost nailed it down. As I understand it, the chemical potential is the change in energy associated with the addition of one...

Hi all, I've been looking through some code for semi-classical transport characteristics of solids and one of the features it can do is artificially "dope" the system by adding in charge carriers. However it seems a bit unstable so I had a peek to see what they actually did to change the...

Hello. There is no agreement on the meaning of terms electrochemical potential and chemical potential (see for example http://web.mit.edu/6.730/www/ST04/Lectures/Lecture26.pdf"). While proper definitions would call chemical potential to \mu\equiv\left(\frac{\partial U}{\partial...

I don't know where the 1/2 comes from in the third image. If I set mu total(up) = mu total up (0), I don't get the 1/2. I'm missing something very simple here. http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110325_214532.jpg?t=1301107797...

hi, How can I show that the chemical potential of an ideal gas µ(T,V ) can be given by: \mu(T , V , N )=k_{b}T\left(a+1+ln(\frac{Nv_{0}}{V})\right)

While useful and unique for reactions or phase transforms, I fail to see how chemical potential brings anything new to ideal gas systems. For example, if chemical potential is described as the quantity the same for 2 systems in diffusive equilibrium, then for ideal gas systems (think 2 boxes...

hi, what is the chemical potential of N2, CO, or NH3 molecules in a gas phase? How to determine it? Thanks.

Hey everyone. I hope someone can help. I'm off on this by several factors so I'm wondering what I may be inferring incorrectly. Homework Statement Express the chemical potential of an ideal gas in termps of T and V: \mu = c_{P}T - c_{V}T\ln T - RT\ln V - s_{0}T + const Homework...

Homework Statement Knowing some gas entropy S= Nk_{B}[ln(\frac{V}{N})+\frac{3}{2}ln(\frac{mU}{3\pi\hbar^2N})+\frac{5}{2}] calculate chemical potential. Homework Equations \mu = -T(\frac{\partial S}{\partial N}) The Attempt at a Solution I multiply all the terms by themselvs...

Chemical potential of a substance i in an ideal solution is given by: \mu_i = \mu_i^0 + RT \log x_i (where \mu_i^0 is a chemical potential of pure substance i and x_i is mole fraction of i) In nonideal solution x_i has to be exchanged with activity coefficient a_i : \mu_i = \mu_i^0 +...

Homework Statement A skateboarder with his board can be modeled as a particle of mass 79 kg, located at his center of mass (which we will study in a later chapter). As shown in the figure below, the skateboarder starts from rest in a crouching position at one lip of a half-pipe (point circle...

Hi Why photon has zero chemical potential. please answer this question clearly.

Hi, Homework Statement Consider a mixture of different gases with N_i molecules each (i=1...k denotes the species). For ideal gases the following relation yields: S(T,V,N_1,...N_k)=\sum_{i=1}^k S_i(T,V,N_i) a)Give explicit expressions for the entropy, the internal energy, Helmholtz free...

Hello, right now, I am learning thermodynamics with Reichl: "A modern Course in Statistical Physics" In chapter 3.C page 100 "classification of phase transitions", the text says: "As we change the independent intensive variables (p, T, x_1,... ,x_l) of a system, we reach values of the...

Can anyone help me. I am very confused about the chemical potential. In the following equation dU = TdS - pdV + u dN, where u is the chemical potential it seems to me that if you add particles to a system you are increasing the energy of that system, i.e. the chemical potential is...

Homework Statement The chemical potential energy in a certain amount of gasoline is converted to kinetic energy in a car that increased its speed from 0 mph to 32 mph. The car accelerated to 64 mph. Compared to the energy required to go from 0 to 32 mph, the energy required to go from 32 mph...

Homework Statement Derive the following: \mu_i=T\left( \frac{\partial S}{\partial n_i}\right)_{U,V,n_j\not=i} \mu_i is the chemical potential of the ith component G is the Gibbs free energy Homework Equations dU = TdS - PdV + \sum_i \mu_i dn_i \mu_i =...

Homework Statement Calculate the change of chemical potential of CH4 in a transformation from the initial state using the ideal gas law. σi={pi=1atm, Ti=298.15K} to the final state σf={pf=100atm, Tf=400K}. any ideas?

Hi there, i've already read some topics in this forum about the fermi-energy/chemical potential. I've also read the article "The chemical potential of an ideal intrinsic semiconductor" from Mark R. A. Shegelski which made the whole thing a little bit more clear to me. but there are some...

Homework Statement Find the three equations of state for a system with the fundamental equation U =(vo\theta/R2)*(S3/NV) For this system, find chemical potential as a function of T,V, and N. Homework Equations \mu= chemical potential \partialU/\partialS = T...

Hello Guys, I'm searching for the best physical definition for the "Chemical Potential" as an energy, what I know is that it's a constant set through Lagrange multiplicands which is set to sustain the number of particles. Actually I'm still not convinced with that, it's an energy, and should...

Homework Statement Hi all. The chemical potential is defined as being the amount of energy one has to remove from a system in order to keep its enotrpy and volume constant when one particle is added to the system. Is this amount of energy the same energy as the energy of the added...

I'm trying to derive a low temperature series expansion for the chemical potential of a weakly interacting Fermi gas. The starting point is, of course, the Fermi-Dirac distribution function (p is the particle momentum): f(p) = \frac{1}{e^{\beta(\epsilon(p) - \mu)}+1} , where, in the...

in a Fermi gas, we know that when the temperature is much less than the Fermi energy, it becomes a degenerate gas. does this mean the chemical potential of the system be very large?

Consider a photon gas in equilibrium with a material cavity (something like a furnace). Why exacly the chemical potential of those photons is zero? The usual handwaving argument is 'because photons are easily created and destroyed' whatever that means. Hydrogen and Oxygen are 'easily created...

Homework Statement For a given phenomena of macroscopic particles. If we model it using the canonical ensemble then we get a certain chemical potential u. But if we model it using the Grand Canonical system, we get a varying chemcial potential that depends on the average number of particles...

can someone simply describe the definition of the chemical potential?

Why for systems containing several components and phases does it require that the chemical potential of ecah component must be idential in every phase?

Consider a solution of particles of type A and B with the following Gibbs potential G(P,T,n_A,n_B)=n_A g_A(P,T) + n_B g_B(P,T)+ (1/2)\lambda_{AA}n_A^2/n + (1/2)\lambda_{BB}n_B^2/n + \lambda_{AB}n_A n_B/n + n_A RT \ln(x_A) + n_B RT \ln(x_B) where the n_i's are the number of moles with x_i=n_i/n...

Hi all, I have a question about the chemical potential \mu from statistical physics: Why is the chemical potential \mu for a photon gas (or phonon gas) zero? Thanks in advance Edgardo