Equilibrium Definition and 1000 Threads

Canonical ensemble can be used to derive probability distribution for the internal energy of the closed system at constant volume ##V## and number of particles ##N## in thermal contact with the reservoir. Also, it is stated that the temperature of both system and reservoir is the same, i.e...

Hi there, this question has already been discussed in this forum, however I do not know how to proceed further and if my reasoning is correct. I start by imagining a downard displacement of the 1kg weight. As a consequence of this, block A moves upward and to the right. Also, block B moves...

Pathria, Statistical mechanics, pg 93 "We consider the given system ##A## as immersed in a large reservoir ##A'##, with which it can exchange both energy and particles. After some time has elapsed, the system and the reservoir are supposed to attain a state of mutual equilibrium. Then...

If there weren't phase changes occurring I know that the temperature equilibrium would be ##T_e=\frac{m_{ice}c_{ice}T_{ice}+m_{w}c_{w}T_{w}}{m_{ice}c_{ice}+m_{w}c_{w}}##. Now, by repeating the reasoning to get the above formula (##\sum \Delta Q=0##) and adding the phase changes of the water...

Hello we learned about the chemical equilibrium and how to write it's formula in the case of liquid and gaseous phase , what about a reaction involving different phases ? like this one : how do we write the formula for the chemical equilibrium ? do we just ignore the carbon ,is there any rules...

Hello i am trying to solve a problem set about chemical equilibrium , the issue is that my results don't correspond to the correction . can someone tell me what is wrong with my answer , thanks here is the problem and his correction : here is my answer :

Hello , i am a little confused about this exercise because we talk about gases reaction and we are asked about the concentrations P.S : i have other questions that depends on your answer . Thanks .

Hi all , please refer to the picture regarding my working. please correct me if My working is wrong. I am quite confused about the positive and negative sign in equation

"... two physical systems [seperated by wall], A1 and A2. A1 has ##\Omega_{1}(N1,V1,E1)## possible microstates, and the macrostate of A2 is ##\Omega_{2}(N2,V2,E2)## " "... at any time ##t##, the subsystem ##A_{1}## is equally likely to be in anyone of the ##\Omega_{1}\left(E_{1}\right)##...

I am performing extraction flash calculations for 4 component and 2 phase system. For anyone somewhat shaky with what extraction flash calculation is; extraction is performed, feed composition is known and we are calculating compositions of both phases at equilibrium, mole fraction of every...

Could I please ask where I have gone wrong with my reasoning in the following question: The answers in given in the book are: (1/2)W tan(Ө) W vertically (1/2)W tan(Ө) horizontally Here is my diagram: Considering the system as a whole: (In the text below "Ya" and "Xa" are the forces at...

I'm designing a table and need to know how much overhang I can have. Assuming the table is completely rigid, is symmetric, and has weight W acting on the CG, how much overhang x can I have? For instance, I know that zero overhang could have L = ∞ (if completely rigid) as the load wouldn't be...

I tried solving it but I don't know how to start because I think that the given values are insufficient. I first tried to compute for individual forces of C, D, and F but I can't their values.

Is there a standard way to measure how far a system is displaced from equilibrium that can be applied to all physical systems? So, for example, a ball that is kicked, a spring that is stretched, a liquid that’s heated, and a charged battery are all systems that are displaced from equilibrium. I...

Hi, I have an issue with understanding the body forces in the context of FEM simulations. I am using freefem to do the simulations. So I took a simple unit cube, fixed the displacements at side ##x=0## and prescribed a displacement ##u_x = 0.025## at ##x=1##. If required, the entire script is...

Im not able to understand the derivation equations and all please. $$ \begin{aligned} \mathrm{HA}+& \mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{A}^{-}+\mathrm{H}_{3} \mathrm{O}^{+} \\ K_{\mathrm{a}} &=\frac{\left[\mathrm{A}^{-}\right]\left[\mathrm{H}_{3}...

$$ \begin{array}{c} \mathrm{HA}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{A}^{-}+\mathrm{H}_{3} \mathrm{O}^{+} \\ \mathrm{K}=\dfrac{\left[\mathrm{A}^{-}\right]\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]}{\left.[\mathrm{HA}] \mathrm{H}_{2} \mathrm{O}\right]} \quad...

Say there is a gas made up of two gas molecules: Molecule A and Molecule B. Molecule A has a mass: ma and mole fraction: na. Molecule B has a mass: mb and mole fraction: nb. The gas is at thermal equilibrium and has a constant temperature throughout itself (T) everywhere. It is placed in a...

Reif, statistical physics "The equilibrium macrostate of a system can be completely specified by very few macroscopic parameters. For example, consider again the isolated gas of ##N## identical molecules in a box. Suppose that the volume of the box is ##V##, while the constant total energy of...

When I use Lagrange to get the equations of motion, in order to find the equilibrium conditions I set the parameters q as constants thus the derivatives to be zero and then calculate the q's that satisfy the equations of motion obtained. In ordert to check about stability I think I need to add...

If I choose my axis of rotation for torque analysis to be the left-end of the plank, I can get the correct results. If I instead choose the com point -- I run into a dead end. Is there a way of a priori knowing this would happen? Thank you.

Hello! I've recently encountered this problem https://www.physicsforums.com/threads/need-major-help.117630/ and solved it and I'm stuck at choosing between 2 solutions. I don't understand why do we need to plug in 0.39 and 0.65 to (1-2x) and NOT to (1-2x)^2. I mean, we were given 2NO2, not just...

For this problem we are asked to find the tension in the cable BE and the compressive force in beam CE. We are given that ## \angle C = 40 \circ##. We are also given that CE = 10 meters and vertical BC = 6 meters. My solution is to find BE using the law of cosines, from which I get $$BE =...

Consider a PN junction doped with say phosphorous on the N side, and Boron on the P side. Initially, there is an opportunity for the electrons just below the N conduction band to drop to the lower available energy states just above the P valence band. This leaves the N side positively charged...

Hello, I'm trying to build a custom made fridge made by a cube by 120cm on each side. The material used to isolate the cube will be some polystyrene panels, with thickness s=4cm. Let's imagine to cool the dry air inside in order to reach the internal temperature of 8 degree Celsius, while the...

This is an offshoot of @Angela G 's thread. I don't want to hijack her thread so I decided to create a new one. Original thread https://www.physicsforums.com/threads/unstable-or-stable-electrostatic-equilibrium.1007881/ @kuruman @PeroK @bob012345 If you have the time I'd appreciate your input...

I wonder if you could help me with both I'm stuck, I know that in order to see if the electrostatic equilibrium is stable or not at the center of the ring , the potential energy has to be minimum there. I was going to use Laplace eq. but it allows neither minimum nor maximum. Then I also...

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... $$...

I tried to solve it and I got the following, is it correct?

Suppose ##A## and ##B## are two liquids, and intermolecular forces between molecules of ##A## are of magnitude ##f_{AA}## and between molecules of ##B##, ##f_{BB}##. If ##f_{AA}>f_{BB}##, then the pure liquid ##A## is volatile than ##BB##, i.e., the tendencies that the molecules have to leave...

The cylinder will cease to be in equilibrium when the sum of the torques on the cylinder calculated with respect to the rightmost point of contact of the cylinder with the plane will be unbalanced. Now, the liquid is homogeneous and the cylinder has negiglible mass so the forces (normal force of...

Most fundamental equation for VLE is $$ \mu_i^L = \mu_i^V $$ It states that for every component chemical potential must be equal in both liquid and vapor phase at equilibrium. However, in my thermo textbook, this equation is derived for isolated systems while usually when dealing with VLE...

Suppose we add a weak acid HA into pure water, so that upon addition its initial concentration is c. The following equilibria should establish in the system. $$\text{HA}+\text{H}_2\text{O}\rightleftharpoons\text{H}_3\text{O}^++\text{A}^-$$...

1) To be in equilibrium, it must be $$\begin{cases}F_{centr}-T=0\\ T-mg=0\end{cases}\Rightarrow F_{centr}=T=mg\Rightarrow m\omega^2 R_0=mg\Rightarrow R_0=\frac{g}{\omega^2}$$ 2) It is intuitive that this equilibrium is unstable but I don't know how to formally prove this. 3) In ##R_0## the...

I HAVE NO IDEA HOW TO START.ONLY THINGS I KNOW ARE WHAT I RERAD ON THIS THRED. https://www.physicsforums.com/threads/equilibrium-of-a-stiff-plate-on-inclined-planes.947601/I can't continue from there. There are also questions where α=β, α+β=45 and where α=45,β=60.How to make use of the fact...

Hi everyone, I have a fundamental question to the first part of Swendsen's Intro to StatMech and Thermodynamics (book). Suppose we have two isolated systems of volumes ##V_1## and ##V_2##. We distribute ##N## ideal gas particles across the two systems with total energy ##E##. Suppose we bring...

My solution: PV = nRT M = dRT / P M is the weighted average molar mass of o2 and o3 --> M = 32x + 16(1-x), where x is the % by mass of o2 and 1-x is the % by mass of o3. M = 32x + 16(1-x) = (0.168 g/L) (62.36 L*torr/mol*K) (448 K) / (128 torr) = 36.668 g/mol solving the equation gives x =...

My solution: partial pressure of C5H6O3 = mRT/MV = (5.63 g)(0.08206 L*atm/mol*K)(473 K) / (114.098 g/mol)(2.50 L) = 0.766 atm equilibrium partial pressure of C5H6O3 = 0.766 - x equilibrium partial pressure of C2H6 = x equilibrium partial pressure of CO = 3x total pressure = 0.766 atm - x + x +...

Literally, don't know how to start.

$\tiny{b.1.2.3}$ Consider the differential equation $\displaystyle \dfrac{dy}{dt}=ay-b$ Find the equilibrium solution $y_e$ rewrite as $y'=ay-b=0$ then $ay-b=0\implies y_e=\dfrac{b}{a}$ (b) Let $Y(t)=y-y_e$; thus $Y(t)$ is the deviation from the equilibrium solution. the differential equation...

I am studying the finite bending of a rubber-like block, assuming Neo-Hookean response. In the following, ##l_0##,##h##, ##\bar{\theta}## are parameters, while the variables are ##r## and ##\theta##. The Cauchy stress tensor is ##T= - \pi I + \mu(\frac{l_0^2}{4 \bar{\theta}^2 r^2} e_r \otimes...

We know that both the interior and the surface of an electrostatically balanced conductor are equipotential. My question is if when we approach the loaded objects, the surface of the conductor will continue to be an equipotential. If not, then there could be a field line that left the region...

The attachment is the key. I wonder where the (3/8)L comes from. Can someone explain it, please? Thanks.

I think (D) is correct since it is half way between the equilibrium point and and the end point of its motion, it is a quarter of the total distance. How to get (C)?

Hi, actually it's not my homework, I'm just practicing some academic problems after a long break but it seems that I should post this here anyway. Here's a scheme of the problem that I want to solve: The task is to calculate minimum force ##P## for the system to stay in equilibrium. And...

In the solving portion of the textbook, the reasoning of the author in solving this problem is that the net work done on the system is zero because the net force of the system is zero. So my question is how was the system in equilibrium (net force=0)? My thinking is that since it is stated...

Hi. I'm not sure about something related to the equilibrium points (or fixed points) of a non linear ode system solution. As far as I know, to check if an equilibrium point exists, I need to put the function of my ode system equal to zero. Then once the point is found, I can use it to evaluate...