# Questions tagged [equilibrium]

Equilibrium is the condition of a system in which all competing influences are balanced. These can range from forces (static/dynamic equilibrium), to chemical processes (chemical equilibrium) and temperature gradients (thermal equilibrium).

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### Entropy and equilibrium concepts at astronomic scales

I am always puzzled to read here and there discussions dealing with thermodynamic concepts applied to astronomic scales where gravity matters. To my opinion, there is a certain carelessness to go into ...
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### Under thermal equilibrium, spin stay still or oscillate?

Under thermal equilibrium, spin stay still or oscillate? For atoms with inertia, atoms will keep moving even the net forces are zero, they will oscillate with velocities. But spin does not have ...
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### Necessary and Sufficient Conditions for an Equilibrium to be Stable

In the 4th section The condition that convection be absent of the book Fluid Mechanics by Landau and Lifshitz, they give the following statement: For the (mechanical) equilibrium to be stable, it is ...
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### Partition function for a system in local thermal equilibrium

For a system in equilibrium, the partition function is standard. But if the system is in local thermal equilibrium but stationary (i.e. zero or negligible time variation), but the temperature varies ...
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I am quoting from "Equilibrium and non-Equilibrium Statistical Thermodynamics", by M. Bellac. $$Q_{(\alpha, \beta)} = \sum_{N=0}^{\infty} e^{\alpha N} Z_{N}(\alpha, \beta) \hspace{1cm} (3.... • 41 2 votes 0 answers 122 views ### Bifurcation of Van Der Waal equation for real gases Van Der Waal's equation leads to a cubic equation in v of the form$$Pv^3-(bP+RT)v^2+av-ab=0This equation has 3 roots for T<T_C and one root for T>T_C I understand why region ABCDE is ... • 41 2 votes 0 answers 29 views ### How does thermalisation make incoherent waves into coherent ones? Thermalisation is the process by which out-of-equilibrium systems reach equilibrium. Coherence refers to the phases of waves being a constant difference apart. While reading a paper on axion stars, I ... • 2,540 2 votes 3 answers 1k views ### Phase transitions and Helmholtz vs Gibbs Free Energy Gibbs phase rule for Gibbs free energy says that phases during a phase transition must be in mechanical, chemical, and thermal equilibrium, e.g. T_1=T_2,G_1=G_2, and P_1=P_2, where the ... • 762 2 votes 0 answers 517 views ### Timescales of physical and chemical equilibrium Background When describing the behaviour of a reacting systems, we usually don't hesitate to apply property models to relate the local properties of each species. For example, in the case of a gas ... • 1,481 2 votes 0 answers 141 views ### Why dynamic equilibrium exists? We know that at equilibrium Gibbs energy is minimum. We also know that at equilibrium both forward and reverse reactions occur simultaneously, and also we know that for a reaction to be spontaneous ... 2 votes 0 answers 136 views ### Vacancy Generation / Annihilation Time (Relaxation Time) Vacancy Generation/Annihilation Time, Recombination Time and Relaxation Time (\tau) are all synonymously used in atomic physics literatures. They're defined as the time that it takes for vacancies ... • 1,819 1 vote 0 answers 12 views ### Charge separation equilibrium equation for non-rotating blackhole at Eddington limit with spherically symmetric accretion? What is the formula for equilibrium charge on a non-rotating black hole with spherically symmetric hydrogen-1 inflow at the Eddington limit of luminosity based on photon scattering acceleration of ... • 1,327 1 vote 0 answers 227 views ### Container divided by frictionless adiabatic wall: reversible or irreversible process? I have encountered an issue in the following physical situation. Consider a rigid, thermally insulated container divided by a barrier parallel to its base into two parts, left and right, each ... • 423 1 vote 0 answers 64 views ### Show that equal pressure is the maximum entropy state Some introduction and background Consider a thermally insulated reservoir filled with some gas. The reservoir is divided in two by a fixed, thermally conducting wall. Initially, the first compartment ... • 1,006 1 vote 1 answer 103 views ### Calculate new equilibrium of cryogenic LNG tank after addition of new cold LNG Disclaimer: I am not a physicist, but I am trying to unravel this problem and it is interesting me more and more the more I work and think about it. I have the following problem: There is a Cryogenic ... 1 vote 1 answer 45 views ### Doubt on thermodynamics equilibrium Is thermodynamics equilibrium related to mechanical equilibrium in anyway? For eg if the net Torque on a system is not zero does that still mean the system can be in thermodynamic equilibrium? 1 vote 1 answer 30 views ### 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 ... • 11 1 vote 0 answers 24 views ### In a DC motor, why would the rotor oscillate around its stable equilibrium point, had there been a constant current? If I choose to replace the commutator in the motor with two slip rigs like those in the AC dynamo, then when the plane of the motor is normal to the magnetic field, aligning, therefore, the magnetic ... • 835 1 vote 3 answers 145 views ### Phase Equilibrium Conditions In explaining phase equilibrium, my textbook gives an example of two phases (\alpha and \beta) of the same species coexisting together and isolated from the rest of the world. With the total ... • 57 1 vote 3 answers 54 views ### Inelastic static tetrahedron with 3 fixed vertices, and 1 free vertex with an applied force This is a problem I've posed myself, which I cannot for the life of me figure out, despite it clearly having a definite answer. Given: A perfectly inelastic tetrahedron in three-dimensional space ... 1 vote 1 answer 455 views ### If three forces act on an object in equilibrium, they must pass through a common point. How does this generalise? If three forces act on an object in rotational equilibrium, the line of action of each force must pass through a common point (parallel forces satisfy this as they go through a common point at ... • 107 1 vote 0 answers 56 views ### Time-Independent Quantum Hamiltonians and Thermodynamic Equilibrium Suppose we have a time-independent Hamiltonian operator \hat{H} of some system. We know that we can express the canonical partition function of said system as z = \text{Tr}(e^{\beta\hat{H}}) for ... • 439 1 vote 0 answers 41 views ### Terminology for scenario when energy of system E(\theta_1,\ldots,\theta_k) with k real parameters, is minimum whenever \theta_1=c (fixed value) Disclaimer. I'm not a physicist. Consider a physical system whose "energy" E is a function of k real parameters \theta = (\theta_1,\ldots,\theta_k) \in \mathbb R^k. Let E_{\min} be ... • 193 1 vote 0 answers 91 views ### Can someone explain Couple with respect to forces acting on it? Suppose two inequal, parallel and opposite forces P and Q are acting on a body not along the same line, producing a clockwise moment. If the rod on which its acting is massless, then we can extend ... • 1,168 1 vote 2 answers 140 views ### Statics question: Free body diagram help for garage construction project I'm building a climbing training apparatus in my garage that both rests on the ground and hangs by a rope from a hook attached to a ceiling joist. Here are some pictures of builds similar to what I'm ... 1 vote 0 answers 29 views ### A comparative study between individual blocks to one long block In relation to two previous discussions about Newtonian mechanics first asked by esdoublef Free body diagram on a rack of wooden blocks and afterwards silverrahul, Horizontal Rack of blocks revisited ... 1 vote 1 answer 17 views ### Balance of an non-homogeneous object Would a pencil balanced on its tip, remain balanced if the the tip was made of a material twice as heavy than the rest of the pencil? 1 vote 0 answers 49 views ### Minimum energy principle for stars In Townsend's Black Hole lecture notes, he says that at equilibrium, E = E_{grav} + E_{kin} is a minimum, where E_{grav} is the gravitational potential energy -\frac{GM^2}{R} andE_{kin} = nR^...
How big must an asteroid be before gravity makes it round and hydrostatic equilibrium comes into the equation? Let's say that being a round planet requires a radius error of $\frac{\delta R}{R}$ that ...