# What is Equilibrium: Definition and 1000 Discussions

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. ### Classification of Equlibrium Points

I hope this is more properly laid out? We previously established that the stationery points were (1,1) and (-1,1) For this first stage I now need to create the elements of a Jacobian maitrix using partial differentation. I am confused by reference to the chain rule. Am I correct that for dx/dt...
2. ### I Why does reversibility require equilibrium?

my question is short simply why reversibility requires equilibrium?
3. ### Potential of particles moving on a circle attracted by elastic force

I use ##l-1## lagrangian coordinates ##\alpha_1,...,\alpha_{l-1}## . ##\alpha_i## is the angle between ##OP_{i-1}## and ##OP_{i}##. As the length of a chord between two rays with angle ##\alpha## is ##d=2Rsin(\alpha/2)##, I write the potential energy of the system as...
4. ### Static Equilibrium Reaction Question about Fixed Point

For this problem I set ΣFy = -3kN - 0.75kN - 3kN + Ay + By (with By representing the right side vertical force, and Ay representing the left side force). For ΣM, I used the rectangular distributed load of 0.5 kN at 3m from point A as the pivot: ΣM = -3m*Ay - (0.5kN*4m) - 3kN*6m - 5kN*m + By*6m...

6. ### Calculate how much weight the crane could lift

I think the first part is F = mxa? But given the jib is resting on a turntable at a certain distance, does that mean the longer and shorted ends experience different loads? Especially when the shorter end has a 16T counterweight? The second part, I have no idea how to calculate this nor the...

8. ### Pressure inside a sealed container

I do know how to solve this question: We find the equilibrium pressure due to air molecules inside the container (after water has stopped flowing). Then, assuming initial pressure of gas inside the container to be atmospheric pressure, we use Boyle's law to find the new volume of the gas and...
9. ### Mass on a spring from equilibrium

Can someone explain that, when using the formula (Fs=1/2 kx^2) why do we use x=0.1m instead of 0.05m? Seems like a simple concept but why isn't it 0.05m (since 0.05m from equilibrium). Thanks.
10. ### I Question about the Zeroth law of thermodynamics and Equlibrium

I know that if 2 systems A and B are in equilibrium their coordinates doesn't change. Systems are not complicated and be fully described using two separated coordinates X and Y. What will happen if I seprate them using an adiabatic wall? Their coordinates start to change but I cannot...
11. ### I Pulley question -- Three pulleys lifting a mass...

Hi, I have this pulley question, i have to find the force F that needs to be applied to the string to keep the system in equilibrium. I found 150N. Is it correct? T_1= 300N and T_2=150N so F is 150N.
12. ### The Relationship Between Masses and Angles in a Pulley System

The problem is based on a similar thread. In fact, the first question is extremely similar. However, the second question is the one I consider more interesting but I posted the first one too for context. If this was just 1 pulley and two masses, then equilibrium is only possible if both masses...
13. ### I Will Heating a Sealed Container Cause All Liquid to Convert to Vapor?

Please can one explain what is exactly gonna happen if we have closed container and liquid is present in it and we heat from bottom ? Then whole liquid will converted into vapour or not ? But during the phase change both system in dynamic equilibrium. If both phases are in dynamic equilibrium...

15. ### Two charged beads with a third bead in equilibrium

Let a = distance between the charge on the left to the third bead. Since the electric field is equilibrium, we equate the electric field emanating from the left charge to the right charge at the location of the third bead. I want to try to find the ratio of d with a. E=E Kq/(d-a)^2 = K*3q/a^2...
16. ### Thermodynamic equilibrium for systems only open to particle exchange

I am only interested in the initial equilibrium conditions, and I am struggling to convince myself whether that should correspond to the equality of chemical potentials for H2 or an equality of temperatures as well. My work is as below: We take both gases as simple ideal (this is only relevant...
17. ### How to find the equilibrium position of three masses (two of them fixed)?

Question: Suppose that two bodies of masses m1 and m2 are a fixed distance d apart, and that both of them act on a third body of mass m. Find the position of the third body such that the two forces are in equilibrium. I have solved this question and obtained the answer listed in the back of the...
18. ### Keeping a uniform bar in horizontal equilibrium

I'm able to get the force of the top spring (6.75N upwards) by setting the sum of all forces equal to 0 as everything is stationary. Where I'm stuck is starting the second part of the problem. I initially tried setting the sum of torques equal to 0 using the top spring as a lever arm but unless...
19. ### A Deriving Non-linear acoustic wave models, equilibrium state assumption

The standard derivation in obtaining a single wave equation involves making use of the heat equation with a Taylor expansion of the equation of state, then differentiating this equation and the continuity equation with respect to time, and combining with the divergence of the NS equation...
20. ### Understanding the Effect of pH on Benzoic Acid Solubility

Suppose we put benzoic acid in a buffered solution at pH=2. In this condition, it will be almost completely unionized and therefore not very soluble. Conversely, if it is placed in a basic environment, the solubility will be high. But why does this happen? Is there a shift in the acid...
21. ### I Equilibrium between objects at different temperatures?

I've come across a puzzling thought experiment. Consider two black bodies surrounded by vacuum. The surrounding temperature is exactly 0 K. By some ingenious optical device all the radiation from body 1 is focused onto body 2 and vice versa. If left alone sufficiently long the two bodies will...
22. ### Electrostatic equilibrium problem

For this problem, I don't understand why this is impossible. Can someone please help? Many thanks!
23. ### Chemistry Finding equilibrium expression for an equilibrium equation

In the d(i) part, we are asked to write an equilibrium constant. It was mentioned in the chapter that solids and liquids will not be added in the equation. So, I think that there is not going to be any Expression for this reaction as all the reactants and products are liquids. Is my answer right?
24. ### Equilibrium and indicator equation

The equation for indicator is: HIn ⇌H+ + In- Which reaction (forward or reverse) will be preferred when I increase the Alkali. According to me, The reverse reaction should be preferred as the reaction will try to minimize the effect of the change. Hence In- (i.e the conjugate base) will be...
25. ### Finding partial pressure at equilibrium

In the coursebook the question says: The reaction below was carried out at a pressure of 10×10⁴ Pa and at constant temperature. N2 + O2 ⇌ 2NO the partial pressures of Nitrogen and Oxygen are both 4.85×10⁴ pa  Ccalculate the partial pressure of the nitrogen(ll) oxide, NO(g) at equilibrium. In...
26. ### B Heat exchange after thermal equilibrium

In screenshot below, systems A and B are separated by an adiabatic wall initially while each of them exchanges energy with system C via a diathermic wall. Once A and B reach thermal equilibrium with C, then A,B are allowed energy exchange via a diathermic wall, and energy exchange between A and...
27. ### A Remarkable Example of Equilibrium

During a recent visit to the Modern Museum of Art in Fort Worth I came across this remarkable sculpture. It appears to be free standing (no strings attached). I assumed it is screwed into the floor and, for obvious reasons, I didn't poke it to see if it will tip over. My thinking is that the...
28. ### B Understanding thermodynamic equilibrium

My thermodynamics is rusty and my current endeavors demand me to wield it, so here we go: I need a good starting point and/or references to study physical systems in thermodynamic equilibrium. Any references which address the fluid mechanics perspective of said systems are welcome too. Let me...
29. ### SO2 Conversion Equilibrium Curve

Hi... i want to draw Equilibrium curve for SO2 oxidation to SO3, i found following relations but don't know to use them... kindly tell me how to draw Equilibrium curve using these equations or any source on web from where i can get directly SO2 oxidation data Vs Temp? Equations are following...

32. ### Equilibrium of a rigid solid on a rod

Figure: Attempt at a Solution: $$F=k\Delta x=lk\sin \theta$$ $$\delta x=0 \quad \textrm{when} \theta=0$$ $$\sum M_C=0\rightarrow$$ $$\rightarrow Pl\cos \theta -F_yl\cos \theta -F_xl\sin \theta =0\rightarrow$$ $$\rightarrow Pl\cos \theta -Fl\cos^2 \theta -Fl\sin^2 \theta=0\rightarrow$$...
33. ### Chemistry Confusion in relation of Gibbs free energy and equilibrium constant

SO2(g)+1/2O2(g)⇌SO3(g);ΔHo=-98.32KJ/mole,ΔSo=-95J/(mole-K). find Kp at 298 Kelvin? In given question at first Δ G will be calculated using formula ΔG = Δ H – T x ΔS, by putting the given values in formula we get ΔG = -70.01 kJ/mol. Then Keq will be calculated using equation = Δ G = -RT ln Keq...

35. ### I Heat diffusion through grain mash to reach equilibrium

I was reading posts this morning on another forum and came across a question that made me start thinking about physics. Since I've always tried to satisfy my curiosity through reading and trying to learn new things, or trying to remember the things that I've forgotten years ago, I went to...
36. ### A Resolve Discrepancies in Boltzmann's Equilibrium Theory

In Lectures on Gas Theory (Dover Books on Physics) (p. 74), Boltzmann states “In nature, the tendency of transformations is always to go from less probable to more probable states”, by which he means what are now called macrostates. Thus he claims that an ideal gas almost always evolves to the...
37. ### Conducting rod in equilibrium due to magnetic force

I am having problems understanding point (b) so I would like to know if my reasoning in that part is correct and/or how to think about that part because I don't see how to justify the assumption ##v_y=0\ m/s##. Thanks. I set up the ##xyz## coordinates system in the usual way with ##xy## in the...
38. ### I Minimization of thermodynamic equilibrium

Hi, I don't understand what does it mean that at equilibrium the proper thermodynamic potential of the system is minimized. For example on the book Herbert B. Callen - Thermodynamics and an Introduction to Thermostatistics it is written: Helmholtz Potential Minimum Principle. The equilibrium...
39. ### I Concept of Thermal Equilibrium in the Context of Canonical Ensemble

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...
40. ### Virtual Work and Static Equilibrium

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...
41. ### 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...
42. ### 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...
43. ### 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...
44. ### 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 :
45. ### 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 .
46. ### 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
47. ### 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)##...
48. ### 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...
49. ### 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...