Equilibrium Definition and 1000 Threads

Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems.
In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs.
Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium.
A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.
In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.
Though not a widely named "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.

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  1. K

    I Questions about a System in Equilibrium

    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...
  2. L

    Finding equilibrium temperature when there are phase changes

    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...
  3. samy4408

    A question about chemical equilibrium

    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...
  4. samy4408

    Chemistry An exercise about chemical equilibrium

    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 :
  5. samy4408

    Chemistry Confused by an exercise on the subject of chemical equilibrium

    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 .
  6. J

    Stable equilibrium and non stable equilibrium question in electrostatics

    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
  7. K

    I Equilibrium equation if the barrier allows particle exchange

    "... 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)##...
  8. Dario56

    Extraction Flash Calculation - 4 Component and 2 Phase System

    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...
  9. G

    To find the forces acting in a system in equilibrium

    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...
  10. Pawn

    Can someone help me find which object is in static equilibrium?

  11. K

    Tipping Over a Table: How Much Overhang?

    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...
  12. hokage12368

    Equilibrium of a Non-concurrent force system

    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.
  13. P

    I Standard measure of distance from equilibrium for all systems

    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...
  14. S

    Body forces in static equilibrium (FEM issue)

    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...
  15. Huzaifa

    Deriving the Henderson-Hasselbalch equation

    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}...
  16. Huzaifa

    How Do Acid-Base Equilibria Work?

    $$ \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...
  17. A

    I Modeling the concentration of gas constituents in a Force Field

    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...
  18. K

    I The Equilibrium Macrostate: Reif's Statistical Physics

    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...
  19. curiousPep

    Engineering Stability Analysis of Equilibrium Solutions using Small Perturbations

    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...
  20. T

    Choosing an Axis of Rotation for Equilibrium Analysis

    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.
  21. D

    Chemistry Chemical Equilibrium: find concentration from 2 solutions (ICE table)

    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...
  22. D

    Seemingly simple equilibrium problem - force balance

    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 =...
  23. U

    What Explains the Lack of Current in a PN Junction at Equilibrium?

    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...
  24. R

    I Estimating a thermal equilibrium on a custom made fridge

    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...
  25. P

    Equilibrium circular ring of uniform charge with point charge

    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...
  26. A

    Unstable or stable electrostatic equilibrium?

    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...
  27. B

    Calculating particle numbers in diffusive equilibrium of a battery

    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... $$...
  28. Tapias5000

    How do I solve this physics exercise (Equilibrium)?

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

    Different volatilities in ideal solutions?

    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...
  30. L

    A slanted cylinder full of liquid about to fall

    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...
  31. Dario56

    Vapor - Liquid Equilibrium Equation (VLE)

    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...
  32. SilverSoldier

    Approximations in Chemical Equilibrium (add a weak acid HA into pure water)

    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. $$\text{HA}+\text{H}_2\text{O}\rightleftharpoons\text{H}_3\text{O}^++\text{A}^-$$...
  33. L

    Mass m sliding without friction inside a rotating tube

    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...
  34. A

    Equilibrium of a stiff plate on inclined planes

    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...
  35. SchroedingersLion

    A Equilibrium, entropy, probability - Release of constraints

    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...
  36. I

    Chemistry Calculating Kp of o2 and o3 equilibrium

    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 =...
  37. I

    Chemistry Decomposition of C5H6O3 equilibrium

    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 +...
  38. Mcmenhweilleisi

    Equilibrium with the string in the center exactly horizontal

  39. jmao15

    Rod in equilibrium, and find its angle to the vertical plane

    Literally, don't know how to start.
  40. V

    Hydrostatic Equilibrium Problem Involving a Cube and two Liquids

  41. karush

    MHB B.1.2.3 Find the equilibrium solution and....

    $\tiny{b.1.2.3}$ 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...
  42. B

    Finite bending of an elastic block - Equilibrium equations

    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...
  43. A

    Induction in electrostatic equilibrium conductor

    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...
  44. H

    Calculate the block mass in an equilibrium system with two supports

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

    Finding (C): Halfway Between Equilibrium and End Point

    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)?
  46. FEAnalyst

    Friction - problem with one of the equilibrium equations

    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...
  47. NoFaceJack

    Exploring the Equilibrium of a System: Net Force & Net Work

    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...
  48. Z

    Equilibrium points doubt (ODE system solution)

    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...
  49. yucheng

    Where is the equilibrium point of a mass sliding down slacking cord?

    My two questions: The author claims that ##T_1=T_2## and ##\alpha = \beta##, and this is supposed to be clear the force triangle. Why is this so? Is it possible to use calculus of variation to find the lowest point C? That is, by maximizing the triangle ABC (Area of ABC = ##\frac{1}{2}(line...
  50. I

    Chemistry Equilibrium of Methanol Vapor Decomposition

    The solution says that when the effusion rate ratio is multiplied by the equilibrium mole ratio of H2 to CH3OH, the effused mixture will have 33.0 times as much H2 as CH3OH. I don't understand why. I just set the equilibrium mole ratio of H2 to CH3OH as equal to 33.0 times, Why is this...
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