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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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 ...
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Origination of internal forces in a beam under axial loads
Take a prismatic beam and subject it to a tensile loading, assume we are applying a load of 10 N on both of its ends. As we know, the beam stretches by a certain amount on either sides.
And since ...
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Calculate weight distribution on 2D plane
I am trying to figure out how I can have a formula for the weight distribution on a square. But let me just describe what I am doing,
We have the classical horizontal beam support problem
And I we can ...
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Repulsive charges in bounded potential
I'm interested in Centroidal Voronoi tessellation especially on disk.
When I got these diagrams, I thought I saw something like this
Looks like a relaxed distribution of identical charges inside the ...
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Difference between thermodynamical, statistical, and dynamical equilibrium
I have two related questions concerning the difference between thermodynamic, statistical mechanical, and dynamical equilibrium. In particular, I am thinking about the statistical physics of galaxies, ...
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Why is the surface of a static liquid always perpendicular to the direction of net force acting on the liquid as a whole? [duplicate]
In a, let's say rectangular container, the water surface always aligns itself perpendicular to the direction of net force acting on it. Why exactly does it happen?
(For example when this container is ...
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Intuitive understanding of the mechanism of uniform bending moment
So many explanations on uniform bending moment and I can't understand until now how it works. I can somehow visualise that in order to resist the external bending moments created by equal and opposite ...
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How to think about thermodynamic equilibrium in terms of virtual displacements?
I am currently taking thermodynamics and am finding the concept of thermodynamic equilibrium rather difficult to grasp. My textbook gives a definition in terms of the virtual displacement of with ...
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Empirical equivalence of shifted chemical potential $\mu_i$
It is often said that, in classical thermodynamics, entropy $S$ and energy $U$ are defined only up to an additive constant proportional to the total amount of substance $N=\sum_i N_i$ (where the sum ...
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Weight distribution and support polygon
I was working on a problem of supporting an object with sticks and wondering about some use cases that would fail.
My approach is to place the n-sticks (for example 4) under an object with mass m ...
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What happens to entropy and energy when you inject heat into 2 systems in thermal equilibrium?
Below we have a system A and B in thermal equilibrium. What happens to the entropy and energy of the systems when you inject heat into system A and let it equilibriate further? I know that heat will ...
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Is the pressure zero in thermal equilibrium? [duplicate]
In a canonical ensemble, we have $dU=TdS-pdV$. When we are in equilibrium, the energy $U$ is minimized. This implies that $\left(\frac{dU}{dV}\right)_S=0$. Since $\left(\frac{dU}{dV}\right)_S=-p$, we ...
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Thermal equilibrium, heat and temperature [duplicate]
I am just studying thermodynamics for the first time and confused between these three terms
Temperature is defined in terms of thermal equilibrium (from zeroth law of thermodynamics) and thermal ...
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Total temperature when combining two systems of unequal temperature [closed]
I know that intensive properties a characterised by the fact that when you combine two systems (A and B) that have the same value of an intensive property (for example same Temperature) the combined ...
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What is the total energy of newtonian polytrope stars of index $n > 5$?
In classical newtonian theory, we could find a general expression for the gravitational potential energy of a polytrope sphere (of pressure $p(\rho) = \kappa \rho^{\gamma}$, where $\gamma = 1 + \frac{...
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Lower bound of stable equilibrium for mass on rotating ring
Consider a point mass $m$ constrained to move without friction along a ring of radius $R$. The ring rotates with angular frequency $\omega$ about the $z$-axis which runs through a diameter of the ring,...
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System in thermal equilibrium with reservoir
Let's say I was trying to build Statistical Mechanics from scratch. I had studied the microcanonical ensemble and made the following definitions:
$$\frac{\partial S}{\partial E} = \frac{1}{T},$$
$$\...
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How fast do $\rm CO_2$ molecules transfer between air and water at equilibrium?
Suppose a bath of water is in equilibrium with the air above it at temperature T and pressure P. The concentration of $\rm CO_2$ in the air is, say, 400ppm, and the concentration of $\rm CO_2$ in the ...
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How does this tensegrity structure work?
How does this structure work? Where is the centre of gravity in this case?
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What is the equation of state (EoS) of a polytrope in general relativity?
I'm trying to numerically integrate the TOV (Tolman-Openheimer-Volkof) equations, using Mathematica. The code works, but I'm having issues with the polytropic equation of state (EoS). The equations ...
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Intravenous therapy - why does blood come out of my body once the fluid is depleted? [closed]
The other day I wasn't feeling so well so I visited a doctor. He recommended that I take a break and get intravenous therapy so I did. I laid on a bed and the nurse inserted a needle into my left arm ...
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Coordinates of center of gravity in non-uniform gravitational field
The following is a textbook problem where one is asked to find the $x$ and $y$ coordinates of the center of mass AND those of the center of gravity in a non-uniform gravitational field:
The location ...
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Why does a reverse reaction occurs everytime?
In a chemical reaction, I have studied that a reverse and forward reaction occurs every time and neither reactant nor product can be zero.
My question is: if the forward reaction and the backward ...
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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 ...
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Numerically solving the TOV equations: how to find the max radius and mass?
I'm solving the TOV (Tolman-Oppenheimer-Volkoff) equations using Mathematica 13.2, and I'm having some issues at finding the outer radius $r_{\text{max}}$ and mass $M_{\text{max}}$ of the spherical ...
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Same temperature implies thermal equilibrium
A particularly weak formulation of thermodynamics is
Two bodies are said to be in thermal equilibrium if no heat transfer occurs when they are put in diathermal contact. Thermal equilibrium is an ...
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How does a particle in a medium return to its original position in case of sound propagation?
I know that particles don't go from one end to the other, they just vibrate and transfer sound energy to next particle. How do they return to equilibrium again? Do they return just after collision ...
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What is equilibrium position in a pendulum? Will there be only one equilibrium position in the motion of a pendulum?
Equilibrium position of a pendulum is defined as the position where no external force acts on the body and if no force is applied, it remains at rest. In the image, isn't gravity acting everywhere, ...
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2 rods connected at a pivot and attached to a spring
I have a question concerning this problem
First I calculate F1 by taking the origin at F2 and imposing equilibrium for the torque thus getting $ F_1 = \frac{a}{a+b} F $ and similarly for F2, then I ...
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Confusion about thermodynamic equilibrium
I’m studying thermodynamics and statistical mechanics from the book by Kerson Huang. I’m having a conceptual difficulty with the notion of thermodynamic equilibrium.
At the beginning of the first ...
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Conditions for the Virial theorem
I've been investigating the Virial Theorem, and I've found different conditions, some more restrictive than others, for it to be applicable to a given system. According to my professor, said theorem ...
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Does physical equilibrium occur at specific temperature and pressure?
Does physical equilibrium occur at only specific temperature and pressure? Like does equilibrium occur only at $ 1 atm $ and $0⁰C$ between water and ice? If I change temperature or pressure will the ...
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Different definitions of equilibrium in statistical mechanics
Statistical mechanics tries to predict macroscopic behavior of a thermodynamic system from microscopic considerations. Suppose we are dealing with system with phase space $\Gamma = (\Lambda \times \...
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A system can be in motion in thermodynamic equilibrium? [duplicate]
I mean thermodynamic equilibrium implies mechanical equilibrium, but mechanical equilibrium doesn't mean to that the system to be in static equilibrium. For some reason, all the systems I have seen in ...
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What is exactly thermodynamic equilibrium? [closed]
As I wrote in the question, what is thermodynamic equilibrium? From what I understand is a state where the thermal, chemical properties don't change with respect of the time and there is a mechanical ...
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Doubt: Arnold's "Mathematical Methods of Classical Mechanics", pg. 18
I am having trouble understanding the following diagram from pg. 18 of Arnold's book:
I am unable to see why local maxima of the potential energy correspond to unstable equilibria (and, reciprocally, ...
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Identifying minimums in gravitational wells in General Relativity
According to the Newtonian gravitational potential:
$$\phi\left(r\right)=-\dfrac{GM}{r}.\tag{1}$$
We can find the minimum possible point in a gravitational well as the one for which the value of the ...
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Doubt on thermodynamics equilibrium
Is thermodynamics equilibrium related to mechanical equilibrium in anyway?
For eg if the net Torque on a system is not zero does that still mean the system can be in thermodynamic equilibrium?
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Osmotic pressure "equilibrium"?
Consider a box with two compartments separated by a semipermeable membrane. The first compartment is initially at pressure $P_0$ and contains the solvent ; the second compartment is initially at ...
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Difference between Displacement from Equilibrum and Amplitude of SHM
I'm currently studying Simple Harmonic Motion. What is the difference between the amplitude of the simple harmonic motion, and its displacement from equilibrium?
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Equilibrium position for double spring hanging vertically [closed]
I feel a bit daft asking this but how do you calculate the equilibrium position of a system with a spring (spring constant k1) hanging from the ceiling with a mass (m1) attached to the bottom, and ...
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Equilibrium position of $ n $ free charges as polynomials roots
The classic problem of the electrostatic equilibrium positions of a linear system of $ n $ free unit charges between two fixed charges is well known, here an example with $n = 1$.
Few days ago I found ...
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What maximizes entropy? [duplicate]
Liouville theorem states that the phase space distribution function of a system remains unchanged with the system evolution,
$$
\frac{\text{d}\rho}{\text{d}t}=\frac{\partial \rho}{\partial t}+\sum_{i=...
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Terminology of different equilibria?
I've heard many equilibrium terms:
Translational equilibrium
Rotational equilibrium
Static equilibrium
Dynamic equilibrium
The different terminology is slightly confusing. My understanding is as ...
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Free body diagram of two cards leaning against each other [closed]
here is my body diagram:
he have the two weights two normals and two frictions however I think I am missing something becaused I only have cosine components when analysing the torque eq with respect ...
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Deriving chemical equilibrium constant from non-reacting or reacting ideal gas mixture partition function?
Given a chemical reaction of ideal gasses:
A <-> B
From my understanding, there are two partition functions that you can write depending on whether A and B can react to form each other.
Non-...
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Why the harmonic series appears when we stack a pile of books?
lets say we have some books resting on the floor.I am trying to find the maximum protuberance that the books can achieve.we see that the books on top of the initial book must have the center of mass ...
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How can two black holes merge without violating No Hair? [duplicate]
Before two black holes merge, their individual event horizons must be perfectly spherical due to the No Hair theorem. If they weren't they'd be betraying information about the inside. After merging, ...
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Do chemical potentials stay constant in chemical equilibrium?
I am uncertain whether chemical potentials stay constant during chemical equilibrium.
Consider a closed container divided into two parts 1 and 2 filled with ideal gas particles. The barrier between ...
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Equilibrium of rods and stress
Reading through Theory of Elasticity, Landau & Lifshitz, I got stuck in the The equations of equilibrium of rods, on page 82. The part I do not understand is the following:
"We denote by $\...
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