Questions tagged [equilibrium]

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Proof of Thomson's theorem on electrostatics using variational calculus

I'm following a proof of Thomson's theorem but I'm a bit confused when they use a lagrange multiplier to include the charge conservation constraint, could someone explain to me how is this multiplier ...
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2answers
33 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
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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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150 views

Why does the Gibbs free energy not decrease ad infinitum?

I would like to ask which guarantees if the Gibbs free energy has a minimum in closed system (e.g. in a chemical reaction system) at constant pressure and temperature? Why does it not decrease ad ...
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1answer
68 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
28 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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4answers
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Why do most office chairs have 5 wheels?

(Inspired by Why are four legged chairs so common?) I've been wondering for a while... Why do most wheeled office chairs have 5 wheels? My guess would be that while stability vs. simplicity results ...
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2answers
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How does a balancing toy work?

I know that the balancing toys have their center of mass under the axis on which they are balancing. That's why they stay still. But when we give a little tap on it, it re-balances itself. But how ...
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1answer
75 views

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
47 views

Teeter Totter Team Building Game

I recall doing a team building exercise where a team of about 4 people needed to balance a teeter totter, so that neither of the ends was touching the ground. They could achieve this by having the ...
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1answer
22k views

Why charges reside on the surface on conductor? [duplicate]

In a hollow conductor and in a spherical shell the charges reside on its surface and there is no electric field inside it.Please tell me the reason behind it.
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4answers
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Why are excess charges in a conductor at the surface?

I’ve been told that coulomb repulsion pushes excess electrons to the surface of a conductor (i.e. sphere) electrostatic equilibrium, and this symmetry causes the net electric field inside to be zero. ...
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1answer
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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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5answers
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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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1answer
65 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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2answers
193 views

Conceptual Question about Suspension Bridge Forces

Two walkways are suspended from vertical rods. In the first scenario, one long rod supports both walkways and is attached to the ceiling. In the second scenario, two shorter rods are attached to each ...
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2answers
57 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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1answer
171 views

Earnshaw's theorem and Effective potential

Earnshaw's theorm says "no stable equilibrium for any $\frac{1}{r}$ potential field in charge-free space". Now I am confused in some aspects, and I would like some helping hands. 1.) General physics ...
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1answer
238 views

Torque of the contact forces about the centre of mass

A person leans in the opposite direction when he or she lifts a heavy load in one hand. I read a reason for the same in a book. According to the book, if a body is placed on a horizontal surface, ...
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1answer
165 views

Electrical charge equilibrium and the piezoelectric effect

About the piezoelectric effect: if I press a crystal the electrical charges segregate and an electrical voltage appears on the other two faces of the crystal. See this link for example: http://www....
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3answers
86 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
29 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
2k views

Thermal state vs equibilibrium state

Could someone explain what's the difference between a thermal state and an equilibrium state? Or is it even the same?
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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
36 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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1answer
478 views

Why the convexity of $E(S,V,N)$ implies that at thermodynamic equilibrium the energy is minimal?

I do understand that in the case of mechanics for example, if there is a soccer ball inside a "well", at mechanical equilibrium, the ball will be at the bottom of the well. ball http://electron6.phys....
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0answers
60 views

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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0answers
25 views

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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1answer
42 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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1answer
197 views

Neutral conductor and charged insulator brought near each other

What happens when a charged insulator is placed near an uncharged neutral metallic conductor? I know it attracts each other because of charging by induction (electrons redistribute). But would the ...
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5answers
2k views

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
320 views

Entropy irreversibilities

How can we say that a system is reversible or irreversible if not stated? I encountered a book example wherein a piston cylinder device encounters an isobaric process and experiences a transfer of ...
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1answer
304 views

Computational scaling of quantum and classical Monte Carlo algorithms

How does the computational complexity of finding an equilibrium thermal state for a given Hamiltonian at a given temperature scale with system size under classical and quantum Monte Carlo? I know ...
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2answers
254 views

(Two fixed charges add in a third), why does it matter which side I put the third charge if I change signs accordingly?

So the question is "Two charges, 1.0 micro-Coulombs and -3.0 micro-Coulombs, are 10 cm apart. Where can a third charge be located so that no net electrostatic force acts on it?". Now the instructor ...
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2answers
2k views

Angles in a static equilibrium

I have three masses $\left(F_\alpha, \, F_\beta , \, \text{and} \,F_g \right)$ with 2 pulleys, and a wind variable which is in static equilibrium. I have already calculated the appropriate forces for ...
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2answers
49 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
34 views

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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2answers
163 views

Is the rate of evaporation in the below mentioned situation constant when liquid vapour equilibrium is not reached?

i am studying liquid vapour equilibrium and there is the set up (below) for the experiment.The conditions:temperature is constant throughout. in this case is the rate of evaporation of the liquid ...
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1answer
855 views

Mechanical equivalent of heat => transfer from work W to heat Q

Consider the following experiment to determine the mechanical equivalent of heat $\mu = \frac{\Delta W}{\Delta Q}$ Not seen in the picture is a weight with known mass hanging down the cord. When you ...
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1answer
60 views

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
28 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 $...
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1answer
53 views

Is there an analogue of Earnshaw’s theorem for inverse cube force laws?

Earnshaw’s theorem states that point charges cannot be held in electrostatic equilibrium by an electric field. Is there an analogue of this for inverse cube force laws?
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Facing a paradox: Earnshaw's theorem in one dimension

Consider a one-dimensional situation on a straight line (say, $x$-axis). Let a charge of magnitude $q$ be located at $x=x_0$, the potential satisfies the Poisson's equation $$\frac{d^2V}{dx^2}=-\frac{\...
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5answers
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How can I prove that a state of equilibrium is unstable?

In the particular problem I encountered, an electric field was zero at the origin and we were meant to prove that a particle at the origin was in an unstable state of equilibrium. Is it enough to ...
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Entropy derivation question

I’m using Atkins thermodynamics book and he has a section I don’t quite understand. The line I’m particuarly question is the one befor (5.2) where he says “by Kelvins formulation of the second law”. I’...
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1answer
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Figure Description of Equilibrium in a Crystal Lattice

I am reading an Introductory Semiconductor Physics by Parker. The textbook states the following: The ionic crystal itself is formed by the ions coming together in an equilibrium configuration. ...
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2answers
186 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 ...
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5answers
85 views

How does the sea level reach a fixed height? [closed]

Consider a flat body of water on the Earth. On all tiny elements of water in that body, the buoyant force is equal to the force of gravity due to Earth. Now if I introduce the moon to this body, (or ...
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2answers
761 views

Pumping water from a closed column. Will the column get empty or just circualte?

As a picture is worth a thousand words, here is my problem: It is a closed water column with a bit of air in the top section. If I run the pump and make the water flow from IN to OUT, Will the level ...