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Questions tagged [equilibrium]

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38 views

Implication of Earnshaw theorem to the orbit of the moon

Can we apply Earnshaw theorem in circular/elliptical/hyperbolic orbits? I was wondering how did the moon stop at its current stationary orbit. It seems to me the fragments that gave origin to the moon ...
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2answers
54 views

Applying the Clausius Inequality to Three Systems

Suppose we have three systems made up of the same amount of the same substance, $S_1, S_2$ and $S_3$. They start with temperatures $T_1$, $T_2$, $T_3$ such that $T_1>T_2>T_3$. We can place the ...
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What does convergence to equilibrium for the Fokker-Planck equation mean?

I am a math major who recently started to study thermodynamics seriously. I have some confusing points while studying it, so I'd appreciate it if you'd correct me and give me some answers. (1) As ...
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1answer
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How would I go about solving for the magnitude of the force the pivot exerts on the bar?

Assuming the bar Is uniform in density. My idea was: since the system is in both translational and rotational equilibrium. $T\sin\theta = F$ (Pivot on Bar) Solving for $T$ let M = mass of bar let ...
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2answers
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How is energy conserved in terms of “Work”

Basic equation of work is given by $F\cdot s$. When work is done, the energy is stored either in form of potential or kinetic. My question arises when we look at a case of applying $m g$ of force ...
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Showing maximum entropy - minimum energy principles equivalence

I'm reading H. Callen's book on Thermodynamics and I don' t understand his proof that the maximum entropy principle implies the minimum energy principle. As a reminder (chapter 5), Entropy maximum ...
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1answer
43 views

Statics and equilibrium of a rigid body [closed]

A vertical cylindrical container contains within it three identical spheres of equal weight P which are tangent to each other and also to the inner wall of the container. A fourth sphere, identical to ...
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40 views

5 Lagrangian points: why isn't there a line of stability between $L_1$ and $L_4$ and $L_1$ and $L_5$ respectively? [duplicate]

Given the 5 Lagrangian points of two large orbiting bodies: (from wikipedia), why isn't there a line of stability between L1 and L4 and L1 and L5 respectively (as depicted in red in the modified ...
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Energy Band diagram in a exponentially $n$-doped Semiconductor and Space charge neutrality

The doping of an $n$-type semiconductor varies as $N_0\cdot e^{(-x/L)}.$ Find the electric field in equilibrium. Plot the band diagram. Comment on space charge neutrality. I got the idea that in ...
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5answers
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Why do things cool down?

What I've heard from books and other materials is that heat is nothing but the sum of the movement of molecules. So, as you all know, one common myth breaker was "Unlike in movies, you don't get ...
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1answer
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Mean position of particle in a Lennard-Jones potential

I want to compute the mean position $\langle x\rangle_\mathrm{eq}$ (let's say in $1$D) in thermal equilibrium (canonical ensemble) of a particle coupled to another particle via a $6$-$12$ Lennard-...
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2answers
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Arnold's Mathematical Methods of Classical Mechanics and Lyapunov stability

In Arnold's Classical Mechanics of Classical Mechanics, he refers to Lyapunov stability in many of the problems in the second chapter. E.g. on page 20: "Problem: Consider a periodic motion along the ...
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1answer
79 views

Equilibrium points of bounce/instanton solution after Wick's rotation

In Coleman's paper Fate of the false vacuum: Semiclassical theory while working out the exponential coefficient for tunneling probability through a potential barrier, he studies the problem with Wick'...
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0answers
18 views

Equilibrium of a rotating particle

Consider a point like particle rotating in a circle with constant angular velocity. Then there must be a centripetal force ok, now the question is can we say that object in equiliibrium? If your ...
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1answer
91 views

How is 0th law of thermodynamics possible?

If a body of gas A (say at $25\ ^\circ \rm C$) is brought in contact with another body of gas B (say at $10\ ^\circ \rm C$), then B absorbs heat from A until they both reach $17.5\ ^\circ \rm C$ and ...
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1answer
46 views

Mutual Equilibrium (Thermodynamics)

From Wikipedia, https://en.wikipedia.org/wiki/Thermodynamic_equilibrium The second paragraph states that "Systems can be in one kind of mutual equilibrium, though not in others" . Could someone give ...
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1answer
23 views

Equilibrium temperature of a black body when the volume of the black body is changed

If a black-body is at an equilibrium temperature T of a certain volume. If we increase size of blackbody does the equilibrium temperature of the blackbody will change?
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2answers
257 views

Why isn't temperature definable for a single, classical particle? [duplicate]

I read that the relation between temperature and kinetic energy of an ideal gas is only applicable to a large number of particles so that the mean value for kinetic energy has to be considered, so the ...
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1answer
49 views

The transversality axiom in Lieb's Thermodynamics paper

I'm reading The Physics and Mathematics of the Second Law of Thermodynamics and have a question about the T4 transversality axiom which is writtern on page 54. T4) Transversality. if $\Gamma$ is ...
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3answers
136 views

How long does it take for an electron to reach equilibrium with blackbody radiation?

While teaching a course on electrodynamics, I thought of an interesting question that I think deserves some attention. Consider an ensemble of electrons all with momentum $\hbar \mathbf{k}$ ...
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1answer
17 views

Finding saturation pressure of steam in a mixture

Suppose you have a gaseous mixture of nitrogen and pure steam (no liquid water), at temperature $T$ and net pressure $P$. The mole fraction of steam in the mixture is $x$. You are told that the steam ...
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2answers
50 views

Why is the force not shown when the body is split into components?

In the given figure, for ease of determining the reactions, the body has been split. The component figures shows internal forces but not the load P. How is this possible ? (Though the figure does not ...
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0answers
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Potential Energy Graph for Nuclear Force

when you draw PE energy graph wrt to distance between two interacting nucleons, at distance $r$ around 1 fm, graph has the lowest PE and is point of stable equilibrum. For $r >$ around 1fm, nuclear ...
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1answer
28 views

Equator water pipeline flow at sea level?

If a water pipeline was built at sea level eg. Gulf of Mexico and the other end was at sea level in southern Chile, then the pipeline was primed with pumps, would the water then gravity feed and flow ...
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0answers
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Where can I find careful discussions of equilibrium?

I want to know what physical equilibrium is precisely. I'd like to understand dynamical equilibrium vs. static equilibrium, and I'd like to understand approaches to understand non-equilibrium ...
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0answers
47 views

If a string had mass in an Atwood machine, would the objects be at rest?

So I understand that the tension produced by a string in an Atwood Machine is constant throughout the string assuming it is ideal, but what if it wasn't? Wouldn't there be a tension gradient, in which ...
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1answer
45 views

In a truss, where is the reaction force acting on?

A truss, its free body diagrams and also of the pin at C is shown in the figure. Ay and P, in figure II may be equated because they are acting in opposite direction on the same body(the whole truss), ...
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0answers
49 views

Mathematical formulation of the concept of temperature

We were taught the following. Consider three systems $A$, $B$ and $C$, which have exactly two independent variables each, $(X,Y)$, $(X’,Y’)$ and $(X’’,Y’’)$. Thermal equilibrium for $A$ and $B$ is ...
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2answers
34 views

Pressure of a system at the thermodynamic equilibrium

I'm reading a book in which it says that a system is at mechanical equilibrium if the pressure is constant in time but not necessarily uniform in space at any fixed point (for example it can be caused ...
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4answers
59 views

Will friction on tyres due to road still act if the vehicle is moving with constant velocity?

A car moves with the help of friction from ground...while analyzing a car moving with constant velocity..should one consider the frictional force acting at the contact point of road and wheel? If ...
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1answer
71 views

Microstates of the system in microcanonical ensemble

Suppose I have a gas enclosed in a thermally insulated box, and so I suppose, this is an example of a system in a micro-canonical ensemble. Now, I want to understand which microstates of the system ...
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1answer
30 views

Proving that motion of an $n$ dimensional oscillator can be written as a linear combination of “sine waves”

Here is a related question which might provide some context: LINK. Let's consider an oscillator with equation of motion in $n$ dimensions: $$ \frac{d^2}{dt^2} \vec{x} = K \vec{x}. $$ Given that $\...
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1answer
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How does my body temperature stay lower than ambient air temperature if it goes over 37°C?

I know it's because of sweat, but why should the sweat over my skin get heat from the body, cooling it under the ambient temperature, instead of getting it from the hotter air all around me? If I ...
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1answer
53 views

Why charges should go to the surface of conductor? [duplicate]

How can we show that charges should go to the surface of a conductor, assuming that system should minimize its energy? (With no additional assumptions and maybe using variation method!)
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1answer
70 views

Why is detailed balance required for thermodynamic consistency?

why does the Wegscheider condition or detailed balance have to be true for chemical reactions and what does it mean to violate it in terms of thermodynamics? here is an attempt to derive a simple ...
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5answers
560 views

Why does a force divide equally on multiple supports/legs?

Imagine a bridge spanning across two pillars/supports with a weight of $80N$. {Any external forces affecting the system are assumed to be negligible.} We know that the force exerted on these 2 ...
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2answers
62 views

Multiple ropes carrying an object

In this problem, the three objects are identical in shape and mass. The suspended horizontal object is uniform and ropes are attached to the object at same distances (the distance between $T_4$ and $...
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3answers
103 views

Is constant temperature and thermal equilibrium same thing?

Can you give some examples which would reveal whether they are same things or not?
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1answer
36 views

Tension in a string attached to a spring with deformation at a point

I am trying to calculate the tension in a string in the configuration shown in the diagram below. Here is a verbal description of the setup: The string is fixed at one end with the other end connected ...
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1answer
25 views

Can I calculate tension in a preloaded string by superposition when the string is deformed?

I am trying to calculate the tension in a string with preloaded tension after a force is applied to the string as in the diagram below. The string would be under tension prior to the force $F$ being ...
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1answer
37 views

How can a rope's tension be at a maximum as a body is about to move up a slope in the rope's direction? [closed]

Note: I do NOT need this exercise's answer. I have no problem working the math out and noticing the truth of my title. A box of mass 0.5 kg is placed on a plane which is inclined at an angle of 40 ...
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Why symmetry leads to stability?

In the whole course of physics I observed a very common thing present around us which is symmetry. Symmetry leads to stability everywhere. For example:-Pauli's Exclusion principle tends to make the ...
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1answer
43 views

Is $d U = 0$ at thermodynamic equilibrium?

At thermodynamic equilibrium, there is thermal, mechanical, and diffusive equilibrium. Does this imply: $$d\mu = dT = dV = 0$$ $$dU = TdS - PdV \implies dU = TdS$$ Here, I know entropy is maximum, ...
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An attempt at justifying effects of minima for Gibbs free energy and Helmholtz free energy

I'm trying to justify that at constant volume, thermal equilibrium is achieved at a minimum of the Helmholtz function. For any thermodynamic process, $$dF = dU - TdS - SdT$$ $$\text{if $dF = 0$}$$ ...
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5answers
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Is thermodynamics only applicable to systems in equilibrium?

So I was going through callen's thermodynamics book and their he says that thermodynamics is only applicable to systems which are in equilibrium and that naturally raised a few questions in my mind ...
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2answers
56 views

How to find Lagrange point $L_2$ of the Earth-Moon system?

I was tasked in my programming lesson to find a value of L1 correct to 5 significant figures, but in my discussion section I began to wonder why there was no second solution to the equation I was ...
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1answer
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Trying to understand the derivation of the Gibbs adsorption isotherm

I have looked at several deritions online, and the clearest I have found is that on the Wiki page The problem being considered is that of two phases, with an interface of a given area between them. ...
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1answer
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Earnshaw's Theorem in Chemical Bonds

Earnshaw's theorem says that: A collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. I also know ...
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1answer
29 views

Static equilibrium (possibility)

In static equilibrium for a ladder leaning against the wall it is supposed to rotate about a point. Why we are not assuming it to slide down as in our practical life?
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1answer
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Does this example contradict Earnshaw's theorem in one dimension?

This is basically a continuation of the post here. Consider electrostatics in $1$-dimension (say, the $x$-axis). Now consider a positive charge $+q$ located at $x=0$, and two equal negative charges $...