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 ...
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 ...
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 ...
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 ...
23
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5answers
7k views

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 ...
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/...
22
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8answers
32k views

Why does maximal entropy imply equilibrium?

From a purely thermodynamical point of view, why does that entropy have to be a maximum at equilibrium? Say there is equilibrium, i.e. no net heat flow, why can the entropy not be sitting at a non-...
19
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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 ...
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 ...
13
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7answers
2k views

Why doesn't an object, despite having a non-zero potential energy stored in it, fall by itself from the elevation?

When an object is at a certain height, it has some energy stored in it as we have done some work on it to get it to that height. So when it already has energy, then why doesn't it fall off from the ...
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",...
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 ...
12
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6answers
2k views

Why do atoms tend towards electrical stability?

If an oxygen atom has six electrons, then it has an unfilled orbital and the oxygen atom may share electrons from two hydrogen atoms (and form water) in order to become more stable. But why does ...
12
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1answer
326 views

Understanding Sakharov's third condition for baryogenesis (departure from thermal equilibrium)

I'm struggling to understand Sakharov's third condition for baryogenesis, i.e., a departure from thermal equilibrium. I don't understand what thermal equilibrium means in this context or proofs that ...
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 ...
11
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4answers
510 views

What's the size to talk about thermal equilibrium?

I am confused about what's the time we can talk about the thermal equilibrium? I mean how many particles the system will contain? This link is a lecture note to teach thermal physics following ...
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 ...
10
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5answers
2k views

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 ...
10
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6answers
7k views

If the Earth is in constant motion then why do we say that an object is in a state of rest?

I got this question as my physics class homework for tomorrow. Anyone please help me out. If Earth constantly rotates and revolves, then how can we call an object in a state of rest?
10
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1answer
1k views

Earth as a perfect sphere and an object trying to stand still

I have imagined the Earth as a perfect sphere with uniform mass density and I put an object somewhere between the equator and the north pole at rest with respect to earth. And also in my imaginary ...
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 ...
10
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4answers
784 views

Is “equilibrium state” equivalent to “well-defined state variables”?

Follow up to Intuitively, why is a reversible process one in which the system is always at equilibrium? and How slow is a reversible adiabatic expansion of an ideal gas? Suppose you have a piston ...
10
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3answers
764 views

Adiabatic piston: why is Callen's argument flawed?

This question is related to this one. I would ask you to read that question and my answer to the question itself before answering this one. The problem is the following. In his book Thermodynamics, ...
9
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5answers
5k views

Is there anything in the universe that is completely static? [closed]

Based on my current, admittedly deficient, understanding of physics everything in the universe is in constant change and motion. Is that understanding correct or is there something that is static? ...
9
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3answers
476 views

Maximum entropy at equilibrium for closed system: Local maximum or global maximum?

For a closed system at equilibrium the entropy is maximum. Is this a local maximum or is it a global maximum? I am an undergraduate physics student and it seems that the possibility of entropy ...
9
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4answers
771 views

Thermodynamic equilibrium

I am a bit confused with the description of the thermodynamic equilibrium from my course. By definition the system is in equilibrium if all state parameters are constant in time and there are no flows ...
9
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3answers
506 views

Airplane with banner in a windy day

Will the banner of this airplane be always in the proper direction if the airplane flies in any direction on a windy day?
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?
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 ...
9
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6answers
8k views

How do we perceive hotness or coldness of an object?

Some objects, especially metallic ones, feel cold on touching and others like wood, etc. feel warm on touching. Both are exposed to same environment and are in their stable state, so some kind of ...
8
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2answers
15k views

Understanding the Jacobian Matrix

Taking the example of a two dimensional system, desribred by the following ODE's: \begin{align} \frac{dx_1}{dt}&=f_1(x_1,x_2)\\ \frac{dx_2}{dt}&=f_2(x_1,x_2) \end{align} The Jacobian Matrix ...
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 ...
8
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1answer
313 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 ...
7
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3answers
3k views

What is the state of the equilibrium for a second derivative equal to zero?

Considering a potential energy of $U$, and a displacement of $x$, the force is given by $F=-\frac{\partial U}{\partial x}$. Since equilibrium is defined as the point at which $F=0$, we can express ...
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 ...
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 ...
7
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2answers
10k views

How do simple bird waterers work?

I made a simple bird waterer made from two 1.25L PET bottles. Let's call these two bottles the reservoir and the tray. Setup The tray is a bottle with the top cut off to leave only the bottom third. ...
7
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0answers
92 views

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 ...
7
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0answers
520 views

Can a substance have zero vapour pressure above absolute zero?

According to this Reddit thread, the answer is no, vapor pressure can't be zero when temperature is above absolute zero. I suspect the answer might actually be yes according to a precise definition I ...
6
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4answers
972 views

Is ergodic hypothesis in contradiction with the notion of equilibrium?

From wikipedia: In physics and thermodynamics, the ergodic hypothesis1 says that, over long periods of time, the time spent by a system in some region of the phase space of microstates with the ...
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 ...
6
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2answers
646 views

Does time pass at all for a system at equilibrium

Time by definition expresses itself through the passage of events. But for a system at perfect equilibrium wherein no change occurs does the rate of passage of time decrease to zero because nothing ...
6
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1answer
375 views

Fluids in thermodynamic equlibrium

I am reading about the Euler equations of fluid dynamics from Leveque's Numerical Methods for Conservation Laws (Amazon link). After introducing the mass, momentum and energy equations, some ...
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 ...
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, ...
6
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4answers
727 views

Can a positively charged conductor have negative surface charge density somewhere?

This is a simple question that occurred to me while thinking about electrostatics. Let's consider a positively charged isolated conductor in equilibrium. In general, the surface charge density varies ...
6
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1answer
204 views

Do the stars in a galaxy have a thermal kinetic energy distribution?

I think, there is practically everything given to that: many point-like masses, able to exchange energy pseudo-randomly, and far long enough time to reach a thermodynamical equilibrium. Of course, ...
6
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1answer
339 views

On the stability of black holes

Vera Rubin just passed (RIP) and recent News reviving the theory that the dark matter might be due to (small?) black holes; the idea that smaller black holes may be more prevalent than thought (then ...
6
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2answers
211 views

Confusion in the deduction of inverse square law of current elements

In Maxwell's treatise, he discusses the inverse square law of current elements in the following way: It is observed from the experiment that the circuit B is in equilibrium, i.e. net force on the ...
6
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1answer
158 views

Can you prove the interesting relation in equilibrium thermodynamics?

Problem and background I noted the following interesting relation in a paper discussing the liquid-vapor phase change, in which it was given directly without any derivation and reference: $$d\ln p^\...