# Tag Info

74

The anthropomorphic formulation "tries to" is misleading. Under the effect of ambient noise, matter explores the possible configurations around its current state: e.g., two single hydrogen atoms wiggle around and meet. If they happen to bind, this releases energy which goes away, and we say that the energetic state of this new $H_2$ molecule is lower than ...

36

The error is that you assume that the density distribution is "nearly spherically symmetric". It's far enough from spherical symmetry if you want to calculate first-order subleading effects such as the equatorial bulge. If your goal is to compute the deviations of the sea level away from the spherical symmetry (to the first order), it is inconsistent to ...

31

Arnold Neumaier's comment about statistical mechanics is correct, but here's how you can prove it using just thermodynamics. Let's imagine two bodies at different temperatures in contact with one another. Let's say that body 1 transfers a small amount of heat $Q$ to body 2. Body 1's entropy changes by $-Q/T_1$, and body 2's entropy changes by $Q/T_2$, so ...

27

Consolidating some of the points made in the answers to the question you linked, and comments: When constructing a chair, 4 legs is easy when you use traditional (wooden) construction - 90 degree angles, and easy to make stackable. A little bit harder than three legs because you have to make sure they are all the same length (or the chair will wobble). ...

24

Nature has no preferences, and therefore entropy tends to increase. Sounds paradoxical? The point is that each microscopic state (describing the exact position and velocity of each atom in the system) is equally likely. However, what we typically observe is not a micro state, but a course-grained description corresponding to incredibly many micro states. ...

23

"A state of rest" is a relative term. Relative means - measured in comparison to the things around it. When you sit in a train and sip from a cup of coffee, you can do so because the cup is still relative to you even though both of you might be hurtling through the countryside at 200 km/h. For most experiments, objects can be considered "at rest" if they ...

21

From a fundamental (i.e., statistical mechanics) point of view, the physically relevant parameter is coldness = inverse temperature $\beta=1/k_BT$. This changes continuously. If it passes from a positive value through zero to a negative value, the temperature changes from very large positive to infinite (with indefinite sign) to very large negative. ...

20

It is wrong to think potential energy is stored in the object. The earth pulls the object down, but the object pulls the earth up. They share the potential energy. The object fails to fall down because the tabletop pushes it up. The earth fails to fall up because the bottom of the table legs push the earth down. The table pushes up and down because it is ...

17

To make it fall you need a torque. This torque is provided by the weight force acting on the center of mass of the object and by the offset between the center of mass and the edge of the object. Imagine your domino standing upright then tilt it. You are moving the center of mass. When the center of mass (blue) is on the right of the edge (red) then you have ...

17

This is a consequence of the second law of thermodynamics, which states that In a closed system with fixed internal energy (i.e. an isolated system), entropy is maximized at equilibrium. It can be shown that this statement is equivalent to the following: In a closed system with fixed entropy, the energy is minimized at equilibrium. Callen in his ...

14

Here we would like to calculated analytically Lubos Motl's solution to the first order in the flatness parameter $f$, $$0<f:=1-\frac{b}{a}\approx\frac{a}{b}-1 \ll 1,$$ where $a$ and $b$ are the equatorial and polar radius of the Earth, respectively, and $a>b$. (The $\approx$ symbol will from now on mean equality up to higher-order terms in $f$.) We ...

11

This is really a statistical effect, as pretty much all of thermodynamics. You have two free hydrogen atoms. They tend to move around the space they have, and when conditions are favourable (there's enough energy, the atoms come "close enough" together), they might interact - chemically or otherwise. Now, "enough energy" is the important bit here. When a ...

10

There was some doubt about Lubos' answer (which I've accepted), so this is just a verification. I copied the method Lubos described and found the potential difference for an ellipsoid with different eccentricities. Sure enough, for an oblate spheroid, if you make the center-equator distance a fraction $e$ larger than the center-pole distance, the ...

10

If you made the most perfect cone possible, so that its tip was a single atom, and stood it on the most perfect surface possible (a perfectly smooth, perfectly hard sheet of atoms), and completely removed all forces other than gravity, it would still topple. This is because those atoms are all jiggling around due to thermal motion. This effect fundamentally ...

10

does it also leads to ... No, it doesn't. A simple Counterexample: Consider the figure below (the bar $\textrm {AB}$ and forces $F$ are on a plane parallel to $\textrm {xy}$ plane) We have $\Sigma \vec F=\vec 0$, but, if we calculate vector sum of torques about point $\textrm A$ we will obtain $\Sigma \vec M_A=F (\overline{AB})\vec k\neq \vec 0$ ($\... 9 I'm going to take a slightly different approach and say it's because we defined energy to make it so. In other words, systems "try" to find the lowest energy state because energy is a concept humans invented in order to describe what we observe. This is the reason that for any given set of constraints, you might need a different "energy" to describe the ... 7 First, if${\rm d}S\neq 0$, then the entropy will change, and because something is changing, it's obviously not an equilibrium. If the physical system doesn't maximize the entropy and it's composed of many parts that may interact with each other, directly or indirectly (it's not disconnected), then any path that allows the entropy to be increased (given ... 7 You need to read this paper by Jaynes. I can't explain it as well as him, but I will try to summarise the main points below. The first thing is to realise that the entropy is observer-dependent: it depends on what information you have access to about the system. A finite temperature means that you don't have access to all the information about the state of ... 7 The excerpt from the text forgets to mention that you assume Local Thermodynamic Equilibrium, and not full Thermodynamic Equilibrium, so to make it possible to define point to point (or from region to region) an EoS. If there is no sense of being 'close' to thermodynamical equilibrium, it is simply impossible to talk about EoS, pressure and the like from ... 7 The forces are never balanced, as there is only ever one force - gravity. The key is to remember Newton's second law:$F = ma. Force and acceleration are paired, not force and velocity. Knowing just an object's current velocity tells you nothing about what forces are acting on it. There are two ways to see how the velocity goes to zero. Either the initial ... 6 Some engineering texts use "moment" and "couple" to talk about forces that tend to rotate an assembly (what physicist mean when they say "torque", but the engineers sometimes have a slightly different meaning for that word). A roughly translation guide is... A "couple" is a pair of opposite forces whose points of action are not co-linear. A couple is ... 6 If a plane is flying without any rudder input, then the banner will always fly straight behind the plane, with nose-tail-banner in a straight line, no matter what the speed or direction of the plane and/or wind. The only thing that affects the plane and banner is the flow of air over the control surfaces. How would the banner know that there was wind ... 6 People don't immediately compress because the body is more or less a pressure vessel. It's not a very good pressure vessel for dealing with vacuum, but it's something. It's your body's resistance to pressure that lets you do things like spray bodily fluids (from your mouth, or from your bladder, or from your arteries). When my wife was in labor with my son, ... 6 Revolving around the sun is equivalent to free fall around the sun, so the revolution allows you not to 'feel' the sun's gravity. The rotation of the earth is something that can be measured: (i) a centrifugal force which is a small offset on gravity, and (ii) causes the coriolis force. Both these are small effects, so can often be ignored for laboratory ... 5 Take a hydrogen gas in a magnetic field. The nuclei can be aligned with the field, low energy, or against it, high energy. At low temperature most of the nuclei are aligned with the field and no matter how much I heat the gas I can never make the population of the higher energy state exceed the lower energy state. All I can do is make them almost equal, as ... 5 Strictly speaking there are no reversible processes in Nature; it is an idealization that enables one to get bounds on efficiency of nonequilibrium processes by using techniques of equilibrium thermodynamics only. A reversible process is therefore primarily a theoretical concept for discussing what would happen in a process if dissipation were absent. It ... 5 It takes a lengthy proof, but Lyman Spitzer shows in the second chapter of Physical Processes in the Interstellar Medium (the standard text in interstellar matter studies) that the velocity distribution of interstellar gas particles (which is what forms nebulae) is very nearly Maxwellian - the deviation is less than 1%. Other larger systems, probably not so ... 5 Using the method of images, you can calculate the force between the ring of charge and the sphere. Assume the sphere is on the z axis with it's center on the pointz$, a radius of$R_s$and the ring's radius is$R_r$with a charge density$\lambda$. So$z\$ denotes the center of the sphere. To calculate the force, you can replace the sphere with a charged ...

5

Other than User58220's answer, I'm reading a lot of nonsense here. When you fly an airplane (I and many other people on this site do), when you are cruising in the air, you center the rudder. The plane has no awareness of the movement of the air mass over the ground (wind). The plane has a vertical stabilizer (tail) which causes it to point into its ...

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