Questions tagged [equilibrium]

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66
votes
7answers
8k views

Why is the Earth so fat?

I made a naive calculation of the height of Earth's equatorial bulge and found that it should be about 10km. The true height is about 20km. My question is: why is there this discrepancy? The ...
40
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7answers
4k views

Prove that negative absolute temperatures are actually hotter than positive absolute temperatures

Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in ...
5
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1answer
303 views

How are the Lagrange points determined?

According to Hyper Physics, there are 5 equilibrium, or Lagrange points of the Earth-Moon system and only 2 of them are said to represent stable equilibrium points. This made me think if there is an ...
6
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1answer
1k views

What's the point with equilibrium in Thermodynamics?

All the Thermodynamics books I saw until now state that in Thermodynamics we are mainly concearned with equilibrium states (I know there's "non-equilibrium Thermodynamics", but I'm interested on the ...
-1
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1answer
289 views

Has the zeroth law of thermodynamics ever been proven?

Has the zeroth law of thermodynamics ever been proven? I know the zeroth law of thermodynamics probably follows from the second law of thermodynamics but according to The statistical nature of the 2nd ...
7
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5answers
494 views

Slow thermal equilibrium

I have a question which is inspired by considering the light field coming off an incandescent lightbulb. As a blackbody radiation field, the light is in thermal equilibrium at temperature $T$, which ...
2
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1answer
2k views

Estimate the reaction force on each leg of a 4-legged table

Assume you have a table with four legs with a weight placed somewhere inside the boundary created by the legs. The task is to determine the reaction force at each leg. Here are the problem ...
4
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1answer
3k views

Definitions in thermodynamics: temperature, thermal equilibrium, heat

I'm currently reading Fermi's "Thermodynamics" and I'm trying to grasp the (possibly different) right definitions for temperature, thermal equilibrium, heat. To clarify, I'm looking for definitions ...
22
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4answers
24k views

Why does the nature always prefer low energy and maximum entropy?

Why does the nature always prefer low energy and maximum entropy? I've just learned electrostatics and I still have no idea why like charges repel each other. http://in.answers.yahoo.com/question/...
11
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3answers
9k views

Why can't charge be in a stable equilibrium in electrostatic field?

I am reading Feynman's Lectures volume_II where he discussed the impossibility of the presence of stable equilibrium in an electrostatic field. There are no points of stable equilibrium in any ...
11
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4answers
2k views

How is quantum mechanics consistent with statistical mechanics?

Let's say we have an harmonic oscillator (at Temperature $T$) in a superposition of state 1 and 2: $$\Psi = \frac{\phi_1+\phi_2}{\sqrt{2}}$$ where each $\phi_i$ has energy $E_i \, .$ The probability ...
3
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1answer
993 views

Is there always an equilibrium point in space for gravity?

For instance, for a two-body system, there will always be a point in-between the two in which the forces of gravity completely cancel, and if I were there then I would experience no net force. I ...
6
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3answers
43k views

When a ball is tossed straight up, does it experience momentary equilibrium at top of its path?

This question has been asked many times all over the Internet and answers can be found on places such as yahoo and ask.com, but I'm not satisfied with those answers and I don't trust the validity of ...
3
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2answers
1k views

Is thermodynamic equilibrium static or dynamic?

Suppose a system has two parts, $A$ & $B$. They were initially at different temperatures and hadn't achieved mechanical equilibrium. After attainting thermodynamic equilibrium, do they continue to ...
61
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6answers
8k views

Why does a system try to minimize its total energy?

Why does a system like to minimize its total energy? For example, the total energy of a $H_2$ molecule is smaller than the that of two two isolated hydrogen atoms and that is why two $H$ atoms try to ...
16
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1answer
2k views

Why is (von Neumann) entropy maximized for an ensemble in thermal equilibrium?

Consider a quantum system in thermal equilibrium with a heat bath. In determining the density operator of the system, the usual procedure is to maximize the von Neumann entropy subject to the ...
9
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1answer
28k views

Difference between steady state and equilibrium?

In semiconductor physics, what is the difference between steady state and equilibrium. How analysis of devices varies in these processes?
10
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1answer
19k views

Question on the hydrostatic paradox

The hydrostatic paradox, states that the height of the water in any container is independent of the shape of the container. This does make sense since it is only the height of the fluid ...
2
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4answers
3k views

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. ...
13
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1answer
4k views

Spikes on ferrofluid?

What exactly are the spikes, or peaks and valleys, caused by in pictures such as these Wikipedia states that "From the point of view of magnetic energy, peaks and valleys are energetically favorable",...
8
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6answers
6k views

Why a system should be at its lowest energy state for its stability?

Every possible reaction in chemistry is to attain stability. In physics, the alignment of an electric dipole in an external electric field and in all other physical systems (at least those I study in ...
3
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1answer
223 views

Reaction forces in pyramid stacking of steel coils

I was tasked with solving this problem at work as we are out of coil holders and we bought 140 coils and need to stack them asap. Companies that make the storage holders are on back order for several ...
9
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2answers
3k views

Do airlocks in space decompress violently as they do in movies?

The standard scene follows: The good guys have finally captured the enemies and have them in an airlock chamber on a spaceship. A button is pressed and out they go, violently propelled by the blast of ...
4
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1answer
345 views

Is this formula for the energy of a configuration of 3 fluids physically reasonable?

I have studied for a couple of months now a mathematical model of the energy of a configuration of immiscible fluids situated in a fixed container such that the fluids fill the container. In other ...
2
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1answer
12k views

Kirchhoff law of thermal radiation

Kirchhoff's law of thermal radiation states that for thermal equilibrium for a particular surface the monochromatic emissivity $\epsilon_{\lambda}$ equals the monochromatic absorptivity $\alpha_{\...
0
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2answers
122 views

Balancing Orthogonal Forces on 2D plane with arbitrary placement [closed]

I have a rectangular block in the xy plane with the center of mass that acts in the z direction at an arbitrary place in the plane. I also have 4 legs that support this weight underneath the block. ...
37
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4answers
13k views

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 ...
5
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3answers
5k views

Thermodynamic reversible process

My book says A process is said to be reversible if it is carried out infinitesimally slowly so that in each step thermodynamic equilibrium of the system remains unchanged & any infinitesimal ...
3
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2answers
2k views

Metal sphere and charged ring

I think this is an interesting question, to which I don't really know the answer to. (Also, not a homework question.) Say you have an uncharged metal sphere constrained to move in the z-axis. There ...
13
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4answers
312 views

How quickly should a fluid come to hydrostatic equilibrium?

Let's say I'm holding a one-liter water bottle, full of water, which I then drop. Before dropping the water bottle, the equilibrium is for there to be a pressure gradient in the water canceling the ...
2
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1answer
2k views

Situation of Stable, Neutral and Unstable Equilibrium

Recently, I was reading about stability of equilibrium. I came across the definitions for different types of equilibrium. Neutral Equilibrium: The kind of equilibrium of a body so placed that when ...
6
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1answer
1k views

Intuition behind classical virial theorem

I am continuing to brush up my statistical physics. I just want to gain a better understanding. I have gone through the derivation of the classical virial theorem once more. I have thought about it, ...
5
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2answers
1k views

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{\...
3
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1answer
2k views

Lagrangian formulation of the problem: small oscillations around an equilibrium

I'm having trouble understanding how some conclusions are made in my book. I'm studying from a coursebook based on Goldstein's "Classical Mechanics", here's what's written in my book, with my problems ...
3
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2answers
1k views

Definition of equilibrium in statistical mechanics

Equilibrium statistical mechanics is (amongst other things) about deriving the equations of state of thermodynamic systems (in equilibrium) from a microscopic basis (i.e. starting with a microscopic ...
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0answers
273 views

Three-log problem [closed]

Three uniform round rigid cylindrical logs of the same size and weight are placed on a horizontal plane. The two at the bottom are touching each other, the third one is placed on the top as shown in ...
1
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0answers
269 views

Why is it valid to assume that the liquid-vapour interface is always saturated during evaporation?

For steady state evaporation, I read from two textbooks which simply states that the partial pressure of vapour of interest (say water) at the liquid-vapour interface is equal to the saturation ...
0
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2answers
78 views

Why there is an extra componet of force in this Equilibrium state?

I have a question about the forces on a body at equilibrium. Look to this image: here i draw a man standing with a pen on earth. And I think that I draw all possible forces on it. They are as ...
0
votes
1answer
447 views

Why is it effectively impossible to balance this rectangle block on a triangle block? (See photo)

I've always wondered why it's basically impossible to balance a rectangle block on top of a triangle one like this. This is my nine-year-old giving it a try. I have never in my life gotten it to ...
7
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4answers
1k views

Applying the Maxwell–Boltzmann statistics to astrophysical objects

Quoting Wikipedia: In statistical mechanics, Maxwell–Boltzmann statistics describes the statistical distribution of material particles over various energy states in thermal equilibrium, when the ...
5
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2answers
7k views

What determines the (minimum) angle at which a domino falls over?

Dominoes, when placed upright, remain that way. Sometimes, even if you tip them a little bit, they will go back to their upright position. However, if you tip them too far, they will fall over. ...
1
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1answer
63 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 ...
1
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1answer
3k views

Mechanics question - ladder leaning against a wall

I am struggling with part a) of this question: Here is the solution: In part a) they prove that $F \leq \mu R$ is false for this system. So as $F$ is neither less than nor equal to $\mu R$ it can ...
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0answers
152 views

How long does it take for a balloon to deflate?

Since gas flows from an area of high pressure to low pressure, upon opening an aperture on say a balloon one would expect the contents to diffuse out until both the inside and outside reach a pressure ...
1
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1answer
357 views

Is this system in stable or unstable equilibrium? [closed]

6 positive, identical charges $+q$ are placed in a hexagon. A negative charge whose value I want to determine is placed at the center to keep the system in equilibrium. Which means $dU/dr = 0$. But ...
0
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2answers
1k views

Pressure in deodorant can

Pressure in a deodorant can is greater than the surrounding pressure but still the can is in equilibrium with the surrounding . Why does this happen. If we apply $F = PA$ then $P_{in}A= P_{atm}A$ and ...
0
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1answer
817 views

Taylor expansion of potential energy

According to the book "Applied quantum Mechanics, Anthony Levi", The Hamiltonian of a monatomic linear chain is given by: The first term on the right side comes from the sum of the kinetic energy of ...
0
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5answers
2k views

Why am I not accelerated by the reaction force applied by Earth on me? [duplicate]

Newton's third law says that "to every action, there is always an equal but opposite reaction". And Newton's second law of motion says that, $F=ma$ $=>$ $a=\frac{F}{m}$. People says that If I stand ...
0
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1answer
540 views

Understanding the Boltzmann factor

By a simple dynamical model one can derive the equilibrium distribution of $N = n_1 + n_2$ identical two-level particles which are subject to Boltzmann-like thermal fluctuations. Consider a particle ...
0
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1answer
2k views

Calculating the amount of dissolved gases in a liquid?

The most basic situation, water at room temperature, has dissolved oxygen, CO2, and more. Why is this? How would one calculate how much gas should be dissolved in any given liquid?