Derive Definition and 628 Threads

> The isothermal compressibility $\kappa_t$ of a substance is defined as $$ \kappa_t = -\frac{1}{V} \left ( \frac{\partial V}{\partial P} \right )_T $$ Obtain an expression for the isothermal compressibility of an ideal gas. (PV = RT) in terms of p. I believe that the ideal gas law equation...

I listened to a lecture the other day that some anomalies in observations compared to theory caused Max Plank to derive his famous Constant.

I am trying to derive the Kepler equation: M = E - e * sin(E) where M=Mean Anomaly, e=Eccentricity and E=Eccentric Anomaly. If you drop a perpendicular down from the object to the Perihelion-axis you can take: a * cos(E) = a * e + Recl * cos (TA) where Recl is the Ecliptic radius to the...

Hello Is it possible to derive the Euler–Bernoulli equation: \frac{d^2}{dx^2} \left(EI \frac{d^2w}{dx^2} \right) = q from Navier-Cauchy equations: \left( \lambda + \mu \right)\nabla\left(\nabla \cdot \textbf{u} \right) + \mu \nabla^2\textbf{u} + \textbf{F} = 0 I don't really know where to...

Homework Statement [/B] This graph shows an infinite string on the x-axis. The middle part is deformed as shown. The string is released at time t=0 - give the analytical solution of the problem, i.e. find for t>0 - sketch the string displacement \xi(x) for a sequence of times t. (I'd like...

Homework Statement Hi, I am stuck with this homework. I have been asked to make an equation out of a diagram for V(z) using V=kQ/r equation, where z is a positive axis centred with four negative charges. Here is the diagram. 2. Relevant equation E=F/q F of point charge: F=kQq/r^2 E=kQ/r^2...

On page 51 Peskin and Schroeder are beginning to derive basic Fierz interchange relations using two-component right-handed spinors. They start by stating the trivial (but tedious) Pauli sigma identity...

Homework Statement there are a lot of mathametical and graphical derivations of the three laws of motion but i have been trying to derive the second equation of motion from the first one but i always end hopeless. please help Homework Equations 1st equation v[f] = v + at 2nd...

Homework Statement This is a magnetic force lab for the second semester of a physics lab course. The setup of the lab is as follows. A wire of length L hangs vertically between two contact points and has a mass with mass m attached to the bottom of it. The wire sits between two magnets in...

Hi all, in following the many available derivations of the Boltzmann distribution I was trying to do it by maximizing W, which is N choose n1,n2,...nt., instead of lnW, because it should give the same answer (since W is monotonically increasing with lnW, am I wrong?). So given the two...

This is a Thermodynamics question. I need help in how to derive the Work done in changing from State 1 and State 2. ie: How do you derive the pV Work formula, W= "integral"dW= "integral"pdV

$$y=ax^3+bx^2+cx+d$$ Find the cubic eq whose graph has horz tangent at the points$ (-2,6)$ and $ (2,0)$ $$y'=3a{x}^{2}+2bx+c$$

Homework Statement Derive the function for the acceleration from this function v=√(2P/M)(√T) The answer is √(P/2MT) I have tried many different attempts but I am still unable to reach this answer. [/B] I am sure the process to get to the answer is a simple one but for some reason I am...

Homework Statement Mathematically prove how Newton's Law of Cooling is derived. Homework Equations Newton’s Law of Cooling states that the rate of change of a temperature of an object is directly proportional to the difference between its own temperature and the temperature of its...

I know there are some threads discussing about the Lorentz force equation but this is something different I came across and I couldn't find anyway to derive that formula. To be specific I'm talking about a charged particles in a magnetic field, where F=vqB and everything that is moving has...

For a parallel plate capacitor, the electric field can be written as $$E=\frac{q}{\epsilon_{0}A}$$ In my textbook it doesn't say how this is derived. I wonder how it is derived - i.e. how can one get to this equation from simpler equations?

If I know the mean and standard deviation, but I don't have an original data set, is it possible to reverse calculate a data set that has this known mean and std dev? Is there an excel function I could use to do this easily? I know there could be multiple correct datasets and that's fine, I'm...

If I know the mean and standard deviation, but I don't have an original data set, is it possible to reverse calculate a data set that has this known mean and std dev? Is there an excel function I could use to do this easily? I know there could be multiple correct datasets and that's fine, I'm...

How did Kepler derive his laws of Planetary Motion without knowing about Newton's law of gravitation? Specifically, the first law of planetary motion which says that planets follow elliptical paths - how did he figure that out without the knowledge of the gravitational pull of the sun? Was it...

Hello everybody, Sorry to ask you something that may be easy for you but I'm stuck. For example I have 2 images (size 2056x2056). One image of reference and the other is the same rotated from -90degrees. Using a program with keypoints, it gives me a transform matrix : a=2.056884522e+03...

I've been working through a qft book by Sadovskii (while I wait for my Peskin book to come in) and I've used some later chapters of Griffith's Into to Elementary Particles as an introduction to some qft. My issue with both of these is that, where in classical mechanics we have the Lagrangian...

Homework Statement Derive an expression for the Gunn-Peterson optical depth Tau(λ) for Lyman limit absorption from smoothly distributed intergalactic neutral Hydrogen of comoving density n0 toward a QSO of emission redshift zem. Take the absorption cross section for Lyman-limit absorption to...

Homework Statement Given an NxN symetric tri-diagonal matrix, derive the recursion relation for the characteristic polynomial Pn(λ) Homework Equations Pn(λ) = |A -λI | Pn(λ) = (An,n - λ)Pn-1(λ) - A2n,n-1Pn-2(λ) The Attempt at a Solution This was easy to do by induction, but I am always...

Can the Heisenberg's Gamma Ray Microscope thought experiment derive the Uncertainty Principle precisely? Most derivations I find, the uncertainty is roughly 2h, whereas the uncertainty principle is "hbar over 2". Is there anywhere where there is more precise calculations to obtain "hbar over 2"...

Does anyone know the proof of joint moment generating functions for bivariate normal distributions? M_x,y (s,t)= E(e^(xs+yt))

Homework Statement A positive charge +q is located at the point x= 0, y = -a and a negative charge -q is located at the point x=0, y=a (a) Derive an expression for the potential at points on the y-axis as a function of the coordinate y. Take V to be zero at an infinite distance from the...

Hello, I noticed that the solution of a homogeneous linear second order DE can be interpreted as the kernel of a linear transformation. It can also be easily shown that the general solution, Ygeneral, of a nonhomogenous DE is given by: Ygeneral = Yhomogeneous + Yparticular My question: Is it...

Homework Statement ##x=r\sin\theta\cos\phi,\,\,\,\,\,y=r\sin\theta\sin\phi,\,\,\,\,\,z=r\cos\theta## ##\hat{x}=\sin\theta\cos\phi\,\hat{r}+\cos\theta\cos\phi\,\hat{\theta}-\sin\phi\,\hat{\phi}## ##\hat{y}=\sin\theta\sin\phi\,\hat{r}+\cos\theta\sin\phi\,\hat{\theta}+\cos\phi\,\hat{\phi}##...

Sorry to bring this question up again. @aridno provides a nice formula of the moment of inertia I about the centroid in https://www.physicsforums.com/threads/calculating-polygon-inertia.25293/ as: $$...

Homework Statement Derive the infinitesimal rotation operator around the z-axis. Homework Equations My book gives this equation (which I follow) with epsilon the infinitesimal rotation angle: $$ \hat{R}(\epsilon) \psi(r,\theta, \phi) = \psi(r,\theta, \phi - \epsilon) $$ but I just don't get...

Derive an exact formula (solve the recurrence definition) for the following recursive sequence: $s_n = 2_{s_n-1} - s_{n-2}$ where $n \ge 2$, and $s_0 = 4$, $s_1 = 1$. So I saw someone solving this by making it a differential equation or something? How would you do that? should I do let...

I'm trying to figure out how to derive the equations for Energy from the differential equation corresponding to the (simple and damped) harmonic oscillator. Please note that I don't want to start with the expressions for kinetic and potential energy, I want to derive them. The references that I...

How do i go about deriving a general eqn for the nth term of a sequence provided an eqn of the sum to the nth term is given in terms of n?

question: I came across a question which said: Derive the equation for kinetic energy of a body of mass m and velocity v. What do they mean? Attempt: I actually just wrote that by work energy theorem diff. in KE = work done so Fx = KE $$ max = m \frac {v²-u²}{2x} x = ½mv² - ½mu² $$ each of...

THIS THREAD HAS BEEN MOVED FROM ANOTHER FORUM BECAUSE IT IS HOMEWORK. BUT THERE IS NO TEMPLATE. Hi everyone, The problem gives that a particle moves in a circle with angular velocity ω. I know that r×ω=v, which is the velocity of the particle. However, I am told to differentiate and find τ=Iα...

T=m[1]m[2]g/(m1+m2)

Homework Statement Part A: Derive an expression for the energy needed to launch an object from the surface of Earth to a height h above the surface. Part B: Ignoring Earth's rotation, how much energy is needed to get the same object into orbit at height h? Express your answer in terms of...

Homework Statement I am reading Mathematical Concepts of Quantum Mechanics (Stephen J. Gustafson, Israel Michael Sigal. Second edition). The book would like to find an evolution equation which would lead to the Hamilton-Jacobi equation $$\frac{\partial S}{\partial t}=-h(x, \nabla S) $$ in the...

Homework Statement For a single molecule, derive the internal energy U = 3/2kBT In terms of the partition function Z, F = -kBTlnZ Where Z = V(aT)3/2 Homework Equations Thermodynamic identity: δF = -SδT - pδV p = kBT/V S = kB[ln(Z) + 3/2]The Attempt at a Solution U = F + TS δU = δF +...

In Serway physics, ampere derived Ampere's law(integral B dot ds=uI) with work done on the magnetic charge by magnetic field.(similear with E dot ds) Without using vector calculus, how can derive Ampere's law from Biot-Savart law?

How to derive the field equations from a Gauss-Bonnet Lagrangian?

Homework Statement Hi I need to know the derivation of the equation HT2 = delta HT1 + delta Cp delta T and I'm really unsure of where to find this. Does anyone know the derivation of this relationship? C represents the the specific heat of the substance in question. H represents enthalpy...

I have been recently working with Schwarzschild's solution: ds2= - (1- (2GM/rc2))c2dt2 + dr2/(1-2GM/rc2) + r2(dθ2 + sin2(θ)d∅2) Now, when deriving the various general relativistic tensors for this metric such as the Ricci tensor, I found the calculations to be painfully tedious and monstrous...

Hello there, I want to derive ##U(\theta) ## for electric dipole placed in uniforum electric field $\vec{E} = E\vec{e}_x$ where E is constant. I define the dipole moment as $p = qd$, where $d$ is the distance from the two I write $\mathm{d}W = p\,E\sin\theta \mathrm{d}\theta =...

Hi Guys, please help me. how can i derive the primitive vector of copper oxide (I)? basically this is cuprous oxide having a cubic crystal structure but since it has oxygen in it the directions and magnitude of primitive vector are far different compare to basic cubic structure. also please help...

Homework Statement density matrix : ρ(t)=0.5+0.5*a(t)⋅σ (a is a 3 dimensional vector and σ is paul victor) H=-μ*σ⋅B (B is a three dimensional magnetic field ) and also assume that in t=0 , ρ(0)=0.5+0.5*a(0)⋅σ whats is the motion equation of a(t)? Homework Equations whats is the motion equation...

Homework Statement Use Maxwell's equations to derive the continuity equation. B=Magnetic Field E=Electric Field ρ=Charge Density J=Current Density Homework Equations Maxwell's Equations: ∇⋅E=ρ/ε0, ∇×E=-∂B/∂t ∇⋅B=0 ∇×B=ε0μ0(∂E/∂t)+μ0J Continuity Equation: ∇⋅J +∂ρ/∂t = 0 The Attempt at...

I made this excel file that is basically a calculator. It needs to create a Total price after fees, profit and supplier cost. Most profit margin calculators have you add a percentage for profit... this is not what I want. I have a hard dollar amount. You must know that the entire transaction...

A Monatomic gas passes from state 1 (pressure p1, volume V1) to state 2 (p2, V2). Derive an expression for the change in entropy of a monatomic ideal gas. The required final equation is: ΔS = Cv ln(T2/T1) + nRln(V2/V1) In my attempt, I am retrieving ΔS = Cv ln(T2/T1) + Rln(V2/V1) i.e.; the...

Homework Statement Could someone explain how Legendre polynomials are derived, particularly first three ones? I was only given the table in the class, not steps to solving them...so I am curious. Homework Equations P0(x) = 1 P1(x) = x P2(x) = 1/2 (3x2 - 1) The Attempt at a Solution ...