# Equilibrium Definition and 122 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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8. ### 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...
9. ### Engineering Equilibrium and stability

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...
10. ### 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...
11. ### 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...
12. ### 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. $$\text{HA}+\text{H}_2\text{O}\rightleftharpoons\text{H}_3\text{O}^++\text{A}^-$$...
13. ### 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...
14. ### 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...
15. ### 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...
16. ### Pin joint? Roller?

Summary:: I am doing my structural analysis homework and I can't seem to identify between pin joint and roller. Please take a look at the following exercises and help me understand: 1) In exercise 6.87, the joint at C is a pin joint whereas in exercise 5.63 the joints at the casters are...
17. ### Rotational Equilibrium Problem [SOLVED]

See attached file. Answer is supposed to be 61.25 N, I get 20.09 N.
18. ### Help finding the vertical component of the reaction at C

Hello everyone, For this equation, I have found Ay as 0.677kN by using Ma = 1.5kN(7m)-Ay(15.5m). To find Cy, would I be using the sum of forces to find the answer? For example Fy = Ay - F2 - F1sin55 + Cy = 0 This would then get Cy answer as 2.05kN
19. ### Chemistry Calculate DeltaH between 700K and 800K

Hi all Knowing that ##kp## is: ##k_p=\frac{pO_2.(pNO)^2}{(pNO_2)^2}## And knowing these relationships between the partial pressures, I obtained: At 700 K: ##pNO = 0.872.pNO2## ##k_p=pO_2.(0.872)^2## At 800 K: ##pNO = 2.5.pNO2## ##k_p=pO_2.(2.5)^2## Furthermore it is known that ##pNO + pNO +...

21. ### Calculate the average number of oscillators of an Einstein solid, in the grand canonical ensemble, when q>>N

$$Q_{(\alpha, \beta)} = \sum_{N=0}^{\infty} e^{\alpha N} Z_{N}(\alpha, \beta) \hspace{1cm} (3.127)$$ Where ##Q## is the grand partition function, ##Z_N## is the canonical partition function and: $$\beta = \frac{1}{kT} \hspace{1cm} \alpha = \frac{\mu}{kT} \hspace{1cm} (3.128)$$ In the case of an...
22. ### Think of a body which is at rest but not in equilibrium

When a ball is thrown upward it becomes at rest at maximum height, at this it is not in equilibrium although it is at rest. It is not at equilibrium because force of gravity is acting on it? Still I cannot find good explanation from exam point of view.I also cannot find the figure/diagram.
23. ### Help with understanding this rigid-body equilibrium problem

So here are two problems I have been working with lately: I have solved both, so I don't need the help to find the answers. The thing that confusses me is which object one should choose to apply the equations above. When it comes to the first problem, we apply the equations to the pole, but...
24. ### Chemistry Why do we say that the concentration of solids and liquids are constant?

I was introduced to the concepts like molarity, molality , mole fraction, formality, normality etc. during general chemistry and it was said that these concepts are used to measure the concentration of solutions. But as the thing called Chemical Equilibrium came I was surprised when I read "In...
25. ### Thermodynamic equilibrium with fixed energy/entropy

If you take a system with fixed entropy S0 and let it evolve, it reachs equilibrium. Let Ueq be the energy of the system at equilibrium. Now take the same system with fixed energy U=Ueq (S is not fixed anymore), how do you know that the equilibrium reached is the same as before, that means with...
26. ### A Equilibrium point of matter and radiation density

We want to calculate the ao/a(teq) of the equilibrium point between ρm and ρr (ρm= ρr ) My book solves it this way; ρm(t) / ρr(t)= a(t) ⇒ ⇒ (ρm/ ρr)teq =1 = = (ρm/ ρr)o * a(teq)/ ao I don't understand the a(teq)/ ao part. If ρm(t)= ρο/αo3 and ρr(t)= ρο/αo4 then it should be ρm(t)/ ρr(t) =...
27. ### Normal reactions at the bases of two light supports

For equilibrium, using ##\Sigma \vec F = 0##, we get ##n_1 + n_2 = 300\; \text{N}##. Taking the system as a whole and applying ##\Sigma \vec \tau = 0## about the hinge (pin) at the top from where the load is hung, we get ##n_1 \times (0.8) \times 4 = n_2 \times (0.6) \times 3##, by taking...
28. ### Spring is stretched, then attached to a mass, what is its speed at x?

Dear all, I am back with another Spring problem. I have tried to use the insights I gained from your help last time: https://www.physicsforums.com/threads/find-v-x-of-a-mass-suspended-from-a-spring.972942/page-3#post-6190934 I figured I start with calculating the new equilibrium by ## x...
29. ### The zeroth law of thermodynamics

let's assume I have 2 systems A and B. the surface that describes when the 2 systems are in equilibrium is given by F(a1,a1,...,b1,b2,...) = 0. assuming we can write this surface as A(a1,a2,..)=B(b1,b2,...) why do A and B describes the temperature function of the systems? in class, we...
30. ### Mass hanging from a 2-pulley system

Homework Statement I have a question about the pulley problem in the attachment. Homework Equations This question can be answered using equilibrium of forces, namely Fx = 0 and Fy = 0. The Attempt at a Solution The answer key states that for the sum of the x-components, we should use the...
31. ### Free body diagram problem

Hello everyone. I find the following problem confusing. A board sandwiched between two boards in the figure below weighs 95.5N. If friction exists between the middle and the compressing boards, draw the free body diagram of the middle board. Below I attached the diagram found in the solution...
32. ### Chemistry Equilibrium Partial Pressures

Homework Statement Kc = 4.15 x 10-2 at 356°C for PCl5(g) ↔ PCl3(g) + Cl2(g). A closed 2.00 L vessel initially contians 0.100 mol PCl5. Calculate the total pressure in the vessel (in atm to 2 decimal places) at 356°C when equilibrium is achieved. Homework Equations PV=nRT Kp= Kc(RT)^change in...
33. ### The concentration of B at equilibrium

Homework Statement For the reaction given below, 2.00 moles of A and 3.00 moles of B are placed in a 6.00L container. A(g) + 2B(g) --> C(g) At equilibrium, the concentration of A is 0.246 mol/L. What is the concentration of B at equilibrium? Homework Equations for aA+bB-->cC, K = [C]^c/([A]^a[...
34. ### Can 3 forces of 9N, 4N, and 6N be in equilibrium?

Homework Statement A mass of 3kg is acted upon by three forces of 4.0 N, 6.0N, and 9.0N and is in equilibrium. The 9N force is suddenly removed. Determine the acceleration of the mass. Homework Equations F=ma. The Attempt at a Solution My main problem with this question is that I cannot think...
35. ### Resolving forces: Mass on a string

Homework Statement A mass of 50 grams hangs in equilibrium on a string. The mass is pulled aside and upwards by a force of 0.3N which makes an angle of 30° with the horizontal. Find the angle that the string makes with the vertical and the tension in the string. Homework Equations Body is in...
36. ### Calculating concenteration at equilibrium

Homework Statement 0.1mole of N2O4 (g) was sealed In a tube under one atmospheric conditions at 25°C.Calculate the number of moles of NO2(g) present if the equilibrium N204(g) --->2NO2(g) (Kp=0.14) is reached after some time Homework Equations K=[NO2]^2/[N2O4] 3. The...
37. ### B Equilibrium - Scalar or Vector?

1 Is Equilibrium a Scalar or Vector quantity? 2 What is the unit of Equilibrium? Thanks & Regards, Prashant S Akerkar
38. ### Plasma Pinch Pressure

Homework Statement Prove that in an MHD equilibrium state in a pinch with flux and Bθ(r) and Bz(r), the equation for pressure is; d/dr(P + B2/8π) + Bθ2/4πr - ρ( u2θ/r)= 0 B is the total Magnetic field, uθ(r) the velocity of plasma, ρ= density, and solving in a (r,θ,z) system Homework...
39. ### My Second Post: Change in Magnitude of Normal Force?

Hello, Let us imagine a solid immersed in a liquid in a container such that the density of the liquid is less than the density of the solid. This means that the solid must sink. Let us study the solid when it reaches the bottom surface and is now at rest. The forces acting on the solid when it...
40. ### FBD of an aerogenerator (Windmill)

Homework Statement Good afternoon, I hope someone could help me with this problem, it is killing my head. I have an aerogenerator, I already find the torque excerted by the air (75.8N) and the force transmitted by the gear (1010.6N). The problem comes when I try to draw the free body diagram to...
41. ### Quick clamp wedge/friction lock calculation

I am currently working on designing a linear brake/lock for a completely different purpose but it will be based on the same principle as in a quick clamp shown below. Before building a prototype I do want to make some rough calculations to check dimensions, angles etc. etc. However, I am for...
42. ### For a solution that contains 0.10 M HCN and 0.10 M NaCN, whi

Homework Statement >For a solution that contains 0.10 M HCN and 0.10 M NaCN, which statement is false? A) This is an example of the common ion effect. B) The [H+] is larger than it would be if only the HCN was in solution. C) the [H+] is equal to $K_a$ D) Addition of more NaCN will shift...
43. ### Finding a maximum force in a beam type system before failure

Homework Statement See attached photo Homework Equations Stress = F/A Area = pi d^3 / 4 Sum F h = 0, Sum F v = 0, Sum M = 0 The Attempt at a Solution Hey everyone, after reading the question a number of times and not knowing for certain where to start, I figured because the stress and area...
44. ### 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...
45. ### I Universe equilibration

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...
46. 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...
47. ### 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...
48. 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...
49. ### Tension in Equilibrium

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)...
50. ### 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...