Helmholtz Definition and 158 Threads

Hello everybody :D My question is: given the distribution of the canonical ensemble, how do we get the helmoltz free energy? I think we can't use A = U-TS because we don't know how to write S. So what's the solution? Thanks

Homework Statement I had a lab where we used Helmholtz coils to measure the period of a bar magnet (1/s2) vs output current. The graph of this is a straight line. Using the slope, I am supposed to be able to derive the C constant and then that divided by the intercept is supposed to yield the...

The formula for Helmholtz coil is given by mu*(0.8^1.5)*nI/R, where I is the current, n is te number of coil and R is the radius of the coil. Now assume the bunch of coils have a small 'thickness' w (so it looks like a hollow cylinder with a very small height), and the the two coils are...

what's the relation of the grand potential J=F-\mu N and total Helmholtz free energy of "system and particle environment" F^{tot}? In K. Sekimoto's book "Stochastic Energetics" P182, P310 and P311 (see screenshots in the link): Does it mean the followings:J=lim[F_{tot}-\mu N_{tot}]...

http://en.wikipedia.org/wiki/Helmholtz_decomposition#Derivation how do we go from to also on the next step ∇' just means the gradient with respect to r', right? Also, why do i have to use the dirac delta function? i thought it was only used to deal with discontinuities? also when we say...

If a current is being applied to a solution with mobile ions in it, why don't the cations lose electrons and the anions gain electrons creating neutral atoms like they do in electrolysis, what causes these ions to stay charged and form a charged lager when they could just gain/lose charge and...

edit: wait... I think the discrepancy is that I calculated Coulombs per kg? and the accepted value I was looking at was in abcoulombs per kg. If that is indeed the case, then my answer is indeed close to the accepted value of 1.76 * 10^11 Coulomb/kg. 1. Homework Statement I am trying to...

Hi, I am trying to understand how precisely a voltmeter is used to measure the resonant frequency of a sound wave in a helmholtz resonator. Is it simply that the maximum voltage corresponds to the resonant frequency? A detailed description or external link would be great. Many thanks.

I only took one class of PDE and even though I do remember the relationship between Laplace and Poisson I really do not recall Helmholtz at all. Anyways, I am trying to figure out if my software (a software I found online, FISKPACK) that solves Helmholtz equation can be used to solve Poisson...

Hi there! I have a problem about the proof of an equation in microscopy. I think this is the right section because it is about solving the Helmholtz equation. I'm looking to Wikipedia page http://en.wikipedia.org/wiki/Multislice where they try to solve the Schrödinger equation for an electron...

Hello, I was just after an explanation of how people get to this conclusion: Say you are looking at the Helmholtz equation in spherical co-ordinates. You use separation of variables, you solve for the polar and azimuthal components. Now you solve for the radial, you will find that...

Consider the Helmholtz Equations with a perturbation p(r) [gradient^2 + p(r) + omega^2/c(r)^2 ]u(r,w) = 0 Does anyone know where I can find resources to the solutions/discussion of this equation? I can find many things such that p(r) = 0 , but the RHS = forcing function, but that is not...

To analyze what does the enthalpy, gibbs free energy and helmholtz free energy are used?What is actually meant by usable energy?

The problem is : a) Find Helmholtz free energy F(V, T) of a simple solid. b) Use the result of part a) to verify that (∂F/∂T)v and (∂F/∂V)T are consistent with S(T, V) and P(V, T) in equation P=a0T-b0ln(V/V0) I know: Helmholtz free energy is F=U-TS and dF=-SdT-PdV S=-((∂F/∂T)v)...

Orthogonality of spherical bessel functions Homework Statement [SIZE="5"]Proof of orthogonality of spherical bessel functions The book gave \int_{0}^{a}\int_{0}^{2\pi}\int_{0}^{\pi} j_{n} (\lambda_{n,j}r) j_{n'} (\lambda_{n',j'}r) Y_{n,m}(\theta,\phi)\overline{Y}_{n',m'}(\theta,\phi)...

The problem is : a) Find Helmholtz free energy F(V, T) of a simple solid. b) Use the result of part a) to verify that (∂F/∂T)v and (∂F/∂V)T are consistent with S(T, V) and P(V, T) in equation P=a0T-b0ln(V/V0) I know: Helmholtz free energy is F=U-TS and dF=-SdT-PdV S=-((∂F/∂T)v)...

Homework Statement Prove that F(k•r -ωt) is a solution of the Helmholtz equation, provided that ω/k = 1/(µε)1/2, where k = (kx, ky, kz) is the wave-vector and r is the position vector. In F(k•r -ωt), “k•r –ωt” is the argument and F is any vector function. Homework Equations Helmholtz...

Helmholtz equation:##\nabla^2 u=-ku## is the same form of ##\nabla^2 u=f##. So is helmholtz equation a form of Poisson Equation?

Hi, i just wanted to confirm that i had the concepts right. So, if i was on Earth and i created something out of nothing (please just bear with me..), and i supplied all the heat that the created system had, then the total energy i would be supplying would be the enthalpy right? and if i...

Helmholtz resonator equation. How do I do this?? Please help. L = 0 Vo = 473.17 (I think its cubed though I calculated it from 16 ounces, so I should be cubed right??) A = What I am solving for F = 480 hz V= speed of sound which is 340.19 at sea level If Vo needs to be cubed then A...

I want to find out how wide the port needs to be for specific frequencies. I suck with math. I have the volume, and the frequency, there will be no neck. Can someone break down the step of how to figure out the port. Also, what units are necessary? I want to just use cm, will that be fine if I...

Homework Statement The 4 fundamental equations of thermodynamics are: dE = TdS - PdV dH = TdS + VdP dG = VdP - SdT dA = - PdV - SdT Supose a gas obeys the equation of state P = \frac{nRT}{V} - \frac{an^{2}}{V^{2}} Use one of the fundamental equations to find the change in Helmholtz energy...

Homework Statement Define the Helmholtz free energy as F=E-TS. Show that the internal energy E=-T2\frac{∂}{∂T}(\frac{F}{T})V Homework Equations S=(\frac{∂F}{∂T})V Perhaps \beta=\frac{1}{\tau} and \tau=kBT The Attempt at a Solution E = F+TS E = F+T(\frac{∂F}{∂T})V . . . (some...

I want to verify this, according to Griffiths p 557: \vec{F}(\vec r')=-\nabla U+\nabla\times\vec A ONLY if both ##\nabla U\; and \; \nabla\times\vec A\rightarrow\;0## faster than ##\frac 1 {r^2}## as ##r\rightarrow\;\infty##. But the requirement of ##\vec{F}(\vec r')## is only...

Homework Statement I am attempting the problem below, I might have the correct answer but would appreciate if someone could confirm this (or tell me where I'm going wrong). Consider a statement having 2 states, one at energy 0 and one at energy ε. Find an expression for the Helmholtz free...

I have a math question in this:http://en.wikipedia.org/wiki/Helmholtz_decomposition. If you look at the proof, what is \nabla_x\frac {1}{|\vec x-\vec x'|}\;and\; \nabla_x \times \frac {1}{|\vec x-\vec x'|} My thinking the first one is just the gradient of ##\frac {1}{|\vec x-\vec x'|}##...

Hi, I am working on a quite difficult, though seemingly simple, non-homogeneous differential equation in cylindrical coordinates. The main equation is the non homogeneous modified Helmholtz Equation \nabla^{2}\psi - k^{2}\psi =...

i have an almost square region. By 'almost' i mean the edges are curvy, not completely straight. i now need to solve the Helmholtz equation with Dirichlet boundary condition what is the best numerical method? how is Finite element, though i do not know what Finite element is

Dear all, I have been spending 12 hours on this and cannot seem to come up with a solution. We derive Helmholtz Free Energy (A) from the second law of thermodynamics. dS(Total) = dS(system) + dS(surrounds) we try to express dS(surrounds) with properties of the system. Assuming...

Stability, Helmholtz free energy mathematical relation "proof" Homework Statement I must show that \left ( \frac{\partial ^2 F}{\partial V ^2} \right ) _T=\frac{\frac{\partial ^2 U}{\partial S^2} \frac{\partial ^2 U}{\partial V ^2} - \left ( \frac{\partial ^2 U}{\partial S \partial V} \right...

I am study chapter 5 of An Introduction to Thermal Physics by Schroeder and I am having trouble understanding his explanation of the differences between enthaply, Helmholtz free energy, and Gibbs free energy. Schroeder defines enthalpy of a system as its energy plus the work needed to make...

I'm confused about the condition for spontaneity for the Helmholtz energy. My textbook (McQuarrie, "Physical Chemistry") derives the conditions as follows. We start with the combined law of thermodynamics: dU = δq + δw ≤ TdS – PdV since δq/T ≤ dS dU – TdS + PdV ≤ 0 For a process at...

Homework Statement Number of wraps of coil on magnetic moment in field: 100 - N_c Number of wraps of coil on Helmholtz coil: 140 - N_h Current through magnetic moment: .796A - I_c Area of magnetic moment: .37m - A_c Radius of Helmholtz coil: .1635m - R_h Current through Helmholtz coil to...

Hi, With the condition that 2 helmholtz coils are parallel with each other sharing the same axis in space . . . What are the differences between electrically connecting up the coils in series and in parallel? cheers

Homework Statement By integrating (2-55), over a small volume containing the origin, substituting ψ = Ce-jβr/r, and letting r approach zero, show that C = 1/4π, thus proving (2-58). Homework Equations (2-55): ∇2ψ + β2ψ = -δ(x)δ(y)δ(z) (2-58): ψ = e-jβr/(4πr) The Attempt at a...

Homework Statement By integrating (2-55), over a small volume containing the origin, substituting ψ = Ce-jβr/r, and letting r approach zero, show that C = 1/4π, thus proving (2-58). Homework Equations (2-55): ∇2ψ + β2ψ = -δ(x)δ(y)δ(z) (2-58): ψ = e-jβr/(4πr) The Attempt at a...

Material in context is in a different color (blue) Okay I'd like to first begin by claiming/stating a few things. One I'd like someone with the proper/accurate knowledge to evaluate my idea which may already have existed preceding tonight which is when I thought of applying some things I had...

hello This is a section from Callen, Herbert B - Thermodynamics and an Introduction to Thermostatistics "Any equilibrium state can be characterized either as a state of maximum entropy for given energy or as a state of minimum energy for given entropy. But these two criteria nevertheless...

Homework Statement Find the eigenfunctions of the Helmholtz equation: \frac{d^2y}{dx^2}+k^2y = 0 with boundary conditions: y(0)=0 y'(L)=0 Homework Equations General Solution: y = Asin(kx) + Bcos(kx) The Attempt at a Solution I found that at y(0) that B=0 and that...

Homework Statement In my ab, we were supposed to obtain the horizontal component of the Earth's magnetic field by measuring the period of oscillation of a bar magnet in a known field using the Helmholtz coils, a resistor, and an AC power amplifier. Now during this experiment I had issues with...

Hi guys, I have a question when solving 3D Helmholtz equation derived from Maxwell equations. Normally I will get a plane wave solution. But when I used the method of separation variables for the three components Ex Ey and Ez, I found that the vector k in these three can be different as long...

Hi!This is a quite sophisticated problem, but it’s interesting and challenging! Consider the following case: Let’s say we have a 3-dimensional disk with a radius r_{2} and a thickness d (so it actually is a cylinder with a quite short height compared to radius). We’re interested in solving...

Hi, Consider P = \boldsymbol{\nabla} f +\boldsymbol{\nabla}\times \bold{A} where f and A are scalar and vector potentials, respectively, and P is strictly positive and well behaved, and only nonzero in a domain \mathcal{D}. I want to find how the magnitude of \int \boldsymbol{\nabla} f dV...

Homework Statement I'm interested in the solution of an equation given below. (It's not a homework/coursework question, but can be stated in a similar style, so I thought it best to post here.) Homework Equations A \nabla^2 f(x)-Bf(x)+C \exp(-2x^2/D^2)=0 where A,B,C,D are...

Homework Statement I have a bit of a problem in class. I am attempting to do an assignment on sound in relation to a guitar. For this I need to explain how the guitar is a highly energetic intrument. I do not know if looking at is like a helmholtz resonator is a waste of my time or not but I'm...

Homework Statement Show that the Green's function for the two-dimensional Helmholtz equation, ∇2 G + k2 G = δ(x) with the boundary conditions of an outgoing wave at infinity, is a Hankel function of the first kind. Here, x is over 2d. Homework Equations The eigenvalue...

Is defined as F = U - TS and it is the energy needed to create a system minus the heat it can get for free. But why is the heat that it can get for free given by: Q = TS I know the thermodynamic relation: S = Q/T So in that way I understand it. But how do you know, that the system will be...

I'm having some trouble understanding this concept. Why is it that you sometimes can get heat for free from the environment? Like suppose you have a system, on which you make an energyconsuming proces which creates entropy. Then you subtract TΔS because apparently heat can enter when the entropy...

Homework Statement it is stated in wikipedia http://en.wikipedia.org/wiki/Helmholtz_equation that "Here, G is the Green's function of this equation, that is, the solution to the inhomogeneous Helmholtz equation with ƒ equaling the Dirac delta function, so G satisfies [del^2 +...

First, I find the term "resonance" and its relatives to be used quite loosely. What is the actual definition according to physics/acoustics. An example of its used: The port of a Helmholtz Resonator resonates at the system's resonant frequency. The port itself is not that thing resonating...