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. Mary1995

    Equilibrium Stability: Finding Charge Stability

    Homework Statement The equation x^2+3x-0.45=0 has two solutions x1=0.14 and x2=-3.14, these are supposed to be the locations at which the electric charge is in equilibrium with two other charges, should I use the first derivative to see at which location the charge will be stable? Homework...
  2. N

    How do I calculate the normal force for equilibrium lab?

    I did torque and equilibrium lab report, where I had to hang some weights on a meter stick, which was placed on a fulcrum. There were 3 parts for the lab, with different settings. I am stuck at the last part, where I hang the meter stick with a string over a pulley, and there were 4 weights...
  3. lichenguy

    Conceptual question about frictional force and equilibrium

    A uniform beam of length L and mass m is inclined at an angle θ to the horizontal. Its upper end is connected to a wall by a rope, and its lower end rests on a rough, horizontal surface. The coefficient of static friction between the beam and surface is μs. Assume that the angle θ is such that...
  4. E

    Unhinged -- Static Equilibrium for a Door

    Homework Statement Homework Equations Torque = r x F The Attempt at a Solution I expect the door to fall.
  5. M

    Calculating Forces and Torques in a Basic Equilibrium Problem

    Homework Statement A sturdy wooden plank, 4 meters in length and having a mass of 42 kg, is rests on 2 supports placed 1.2 meters from each end. Suppose a man of 72 kg stands 1 meter from the right end of the board. What are the upward forces on each board? |---L----R-M--| Where L is the left...
  6. D

    Problem in the C.G. and torque equilibrium

    Homework Statement A 40.0 kg uniform platform is suspended by two cables, 2.00 m apart, where the centre of the platform lies midway between the cables. A 5.00 kg paint bucket is placed on the platform, 24.0cm to the right of the right cable, as shown in Figure A2.15. What is the tension in...
  7. A

    How to Solve for T in an Equilibrium Problem?

    Homework Statement Homework Equations The Attempt at a Solution I'm trying to solve this problem but I can't get the Te by itself. Does anyone have any answers as to a direction I should take?
  8. durant35

    I Equilibrium of Universe: Earth vs. Black Hole

    I have a question regarding the process of getting towards equilibrium in our universe. If we imagine a causal patch with our planet at the centre, every planet will redshift away from us an after a while the planet itself will disintegrate, let's call this process the decay of Earth. Eventually...
  9. C

    Equilibrium constant expression; why exponents?

    Hello all. I am wondering why we raise the concentration to the exponent of the stochiometric coefficient. I understand why we take the products of reactants or products. For instance, let me give an example to show where I am getting mixed up. Let's say 2A +3B = 8C as a reversible...
  10. P

    Will a block slide in a moving lift with equilibrium?

    Homework Statement Homework Equations The Attempt at a Solution [/B] Effective gravity = g-a So Frictional force = tension Tension = m(g-a) u 2m(g-a) =m(g-a)
  11. M

    Calculating force to tip over a cabinet (static equilibrium)

    Homework Statement Homework Equations How do you solve for the force in this problem and also the coefficient of static friction and minimum force to tip the cabinet over if the point of application can be chosen anywhere on the cabinet? The Attempt at a Solution I tried setting up tables...
  12. G

    Equilibrium Climate Sensitivity

    Equilibrium Climate Sensitivity - what is the relevance of the word 'equilibrium' - why not 'climate sensitivity?' Hope you can help.
  13. B

    Thermal equilibrium and isolation

    If two objects are at the same temperature, but thermally isolated from one another, are they still considered to be in thermal equilibrium with one another?
  14. M

    Find the tension in the cable and the force the ramp exerts on the tires

    Homework Statement A 5000 kg car rests on a 32° slanted ramp attached to a trailer. Only a cable running from the trailer to the car prevents the car from rolling off the ramp (the car's transmission is in neutral and its brakes are off). Find the tension in the cable and the force that the...
  15. MathematicalPhysicist

    Equilibrium Statistics -- Euler summation formula

    Homework Statement In the calculation in high temperatures of ##Z_{rot} = (\sum_{j=0}^\infty (2j+1)\exp{j(j+1)\theta_{rot}/T})^N##; they use Euler summation formula: $$\sum_{n=0}^\infty f(n) = \int_0^\infty f(x)dx+\frac{1}{2}f(0)-\frac{1}{12}f'(0)+\frac{1}{720}f^{(3)}(0)+\ldots$$ for ##f(x) =...
  16. A

    Spring angles at static equilibrium on application of force

    Homework Statement Two linear springs with stiffness Kh, Kv are attached to a single mass m at right angle to each other, i.e; one of the spring(Kh) is in the horizontal direction(x-axis) and the other(Kv) is in the vertical direction(y-axis). A constant force F is being applied to the mass...
  17. D

    Water molecules effect on Hydrogen bonds in precipitation

    Cheers everyone. Can the amount of water molecules added to a solution impact the formation of a salt with its ions mainly bonded through hydrogen bonds with electrostatic like behaviour? Let me give Some background to the question first: I am studying the precipitation of Phosphorous(P) as...
  18. Pushoam

    Entropy- change & the condition when a system reaches equilibrium

    Homework Statement Homework EquationsThe Attempt at a Solution I didn't understand the last part. At eqbm. ##\Delta S = 0##. This means that the RHS of the eqnn. 14.25 is 0. This doesn't mean that the following eqns. must hold true. ##(\frac 1 T_1 - \frac 1 T_2) =0,.............(1) \\...
  19. V

    I Nuclear statistical equilibrium

    Sorry, I have never found what does it mean Nuclear statistical equilibrium. It is used in any text but exact explanation nowhere. Please explain a physical meaning of it. Thank you.
  20. R

    Equilibrium Question -- Thrust versus Lift....

    Homework Statement Given: Thrust: 103000 N Lift = ? Weight = 86500 N Resistance = ? Homework Equations I'm just to figure out the value of resistance and lift. The Attempt at a Solution I can't seem to figure out a way to find out resistance, but with lift I believe it has something to do...
  21. J

    Rotational Equilibrium Question

    Homework Statement A bar of uniform density, length L, and mass m is suspended by two ropes of tensions T1 and T2 at either extremity of the bar. The bar is tilted such that it makes an angle θ with the ropes. A mass M is resting at a distance l from T1. https://i.imgur.com/vLlAJbe.png If...
  22. Z

    Equilibrium of pistons with different radii (Hydraulics)

    Homework Statement [/B] Homework Equations Force exerted by liquids F=h.d.g.A The Attempt at a Solution
  23. curiosity colour

    Chemical Equilibrium Q: How Does Solution (a) Know PH2S=Ammonia?

    I have a question about the solution (a) in this example, how does it know PH2S is the same as ammonia? is there something I've miss?
  24. S

    Work energy theorem and forces at equilibrium -- Conceptual doubt

    A pendulum of mass m and length l is suspended from the ceiling of a trolley which has a constant acceleration a. Find the maximum deflection θ of the pendulum from the vertical. When I used work energy theorem, I got θ = 2 arctan(a/g). But when I took the equilibrium position and equated the...
  25. D

    I Gibbs Energy and chemical equilibrium

    Hi, i'll apologize for my english in advance, so here's the question. I was wondering about the equilibrium condition for a chemical reaction. We know that a closed system is in equilibrium if the Gibbs free energy's function has a minimun in that point. So, taking Temperature and Pressure as...
  26. M

    MHB Calculate Equilibrium Constant of 2BrCl <=> Br2 + Cl2

    bromine monochloride dissociated on heating the following equation 2BrCl <=> Br2 + Cl2 .9 moles of BrCl were heated in a 5 liter vessel until equilibrium was established . the amount of free chlorine in the mixture was found to be .4 moles calculate the equilibrium constant for the reaction...
  27. M

    MHB Uniform rods and disk in static equilibrium

    i am stuck on question 9 can anyone help me out. thanks
  28. J

    Find the tension in the cable and reactive forces at ground

    Homework Statement A 160-kg utility pole extends 12m above the ground. A horizontal force of 250 N acts at its top and the pole is held in the vertical position by a cable, as shown in the figure (I have attached the photo). 1) draw a free-body diagram for the pole 2) Determine the tension...
  29. D

    Equilibrium volume of two differential van der Waal gases

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  30. math4everyone

    A Equilibrium in system of non-linear difference equations

    I have a little question. I want to know if there is a process in which I can find equilibrium solutions to some system of difference equations. For example, if I have something crazy like $$\begin{cases} x[n+1]=(x[n])^2y[n]+z[n]e^{-ax[n]} \\ y[n+1]= z[n]x[n]+x[n+1]y[n+1]\\ z[n+1]=...
  31. alemsalem

    A Calculating Einstein's coefficients in QFT vs equilibrium

    Einstein predicted constraints on the coefficients of stimulated emission and absorption of radiation by atoms. He did that by assuming that the gas of atoms had to reach thermal equilibrium. For the gas to reach thermal equilibrium the coefficients had to be related in a certain way, otherwise...
  32. esha

    Potential energy and equilibrium

    It is said that a negative potential energy gives stable equilibrium but a positive potential energy gives an unstable equilibrium. why is it so?
  33. U

    Pressure dependence of the equilibrium constant for an ideal gas

    I read in some scripts that equilibrium constant for an ideal gas is not a function of pressure: But that is not generally true! Since: $$\left (\frac{\partial \Delta_{R} G}{\partial p} \right )_{T,\vec{n}}=\Delta_{R} V$$ and $$\Delta_{R} G^{0}=-RT\cdot \ln K$$ it should be: $$\left...
  34. M

    2 body engine, final equilibrium temperate and work produced

    Homework Statement 2 bodies with contant heat capacity C and 2C, are initially at temp T and 2T. if a heat engine executing a reversible carnot cycle operates between the two bodies until their temperatures are equal, what is the final temp of the bodies and how much work is preformed by the...
  35. E

    Basic torque/static equilibrium problem

    Homework Statement Homework Equations sum of forces = 0N sum of torque = 0Nm The Attempt at a Solution Net force has to be already zero (T = mg). But, the torque isn't zero, otherwise this question would have another answer choice. But the gravitational torque should cancel with the tension...
  36. D

    Specific heat in the curve of equilibrium

    Homework Statement Consider a system formed by two phases of a substance that consists of a single class of molecules. Determine the specific heat ##c## of a vapor pressure and temperature ##p## ##T## on the curve of liquid-vapor equilibrium. Consider the steam as an ideal gas. Data: ##c_p##...
  37. Strawberry1711

    Can Total Energy Be the Same in Liquid and Vapour Phases at Equilibrium?

    Homework Statement A liquid is in equilibrium with its vapour at it’s boiling point. On the average, the molecules in the two phases have equal;; provided options are: a. inter-molecule forces b.potential energy c .Kinetic energy d.total energy . Homework EquationsThe Attempt at a Solution ...
  38. B

    Moment Equilibrium in terms of box weight

    Homework Statement The board shown below is being held in equilibrium in the vertical plane by three smooth rods at A, B, and C Determine the magnitudes of forces at A, B, and C in terms of the weight of the body, W. Homework Equations Moment = f*r Here's a diagram The Attempt at a...
  39. durant35

    I Equilibrium chaotic environment

    Cosmological fluctuations from equilibrium are best described in the Boltzmann brain paradox. My question may very well be better suited for statistical mechanics but it has relations with cosmology so I'll post it here. Anyway, it is often stated that BBs will perceive chaotic observations...
  40. D

    B How can anyone explain the universal equilibrium density problem

    With NASA defining this equilibrium density at 9.9 x 10<30 gm/cm3, how can an increasingly expanding universe maintain a steady density as it expands?
  41. karush

    MHB -Identify the equilibrium values y'=5\sqrt{5},y>0

    1000 $\textrm{ Given $y'=5\sqrt{5},y>0$ answer the following questions.}\\$ $\textrm{a. Identify the equilibrium values.}\\ $ $\textrm{Which are stable and which are unstable?}\\$ $\textrm{b. Construct a phase line. Identify the signs of $y′$ and $y′′$.}\\$ $\textrm{c. Sketch several solution...
  42. tom.stoer

    Hydrostatic equilibrium and Navier-Stokes equations

    Is it possible to derive the condition for hydrostatic equilibrium or the Navier-Stokes equation for a self-gravitating fluid - e.g. for water on a planet with non-homogeneous density - based on a variational principle? (the planet itself is assumed to be a fixed hard core not subject to the...
  43. Mateus Buarque

    Simple Harmonic Motion and equilibrium of springs

    The figure below shows a system in equillibrium. The pulley and the springs (both with constants "k") are ideal. The period of oscillation of the mass A is given by: Relevant equations: F = -kx (SHM) I tried to do a "force diagram" and set up some geometric relations but it´s not working.
  44. T

    Why Does Tension Vary Along the Rope in a Hanging Superhero Scenario?

    Homework Statement [/B] Superhero and Trusty Sidekick hang motionless from a rope. Superhero’s mass is 90.0 kg, while Trusty Sidekick’s is 55.0 kg, and the mass of the rope is negligible. (a) Draw a free-body diagram of the situation. (b) Find the tension in the rope above Superhero. (c)...
  45. esha

    Why is degree of ionization inversely proportional to....

    Degree of ionization is the number of particles which dissociate by the total number of particles. if that's the case then higher number of particles should mean higher number of particles which get dissociated. this should also mean higher the concentration the degree of ionization will also...
  46. person123

    Exploring Pulley System Equilibrium: Solving for y when x Changes

    I was working on a pulley system as shown here: The mass on the right and left side is equivalent, and I am solving for when the system is in static equilibrium. Theta is the angle between the rope on either side of one of the pulleys. H and y are both measured from the original position of...
  47. F

    Direction of Normal Force on Object B: A Scientific Inquiry

    Homework Statement The Attempt at a Solution Can somebody please assist me in finding the direction of the normal force exerted on B? (How is normal force at B also normal to the rod? ) There is no hint provided from which I can conclude the direction of normal force. Can somebody please...
  48. M

    Naive Doubt About Thermodynamic Equilibrium

    This is more of a recurring conceptual doubt that I keep on running into when solving thermodynamics problems. We are taught that variations between extensive state variables in equilibrium are given by the following 'fundamental formula': dE = TdS + \mathbf{J}\cdot{d}\mathbf{x} +...
  49. N

    How Many Moles of BaCO3 Dissolve in Water Given Kc?

    Homework Statement Excess BaCO3 is placed in a container containing 5L of pure water. Given the following info: BaCO3 (s) ↔ Ba2+ + CO3 2- and Kc = 5.7E-6 how many moles of BaCO3 dissolve? Homework Equations Kc=(Ba2+ )(CO3 2- ) = 5.7E-6 The Attempt at a Solution solved for x to get .002387...
  50. S

    Assumption of local thermodynamic equilibrium in a fluid

    Moving fluids are generally in a state of non-equilibrium. However, in fluid dynamics, people generally assume a state of local thermodynamic equilibrium and argue that in such a condition, equilibrium thermodynamic concepts such as pressure, temperature, entropy, internal energy etc. can be...
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