# Tag Info

16

The reason is electron degeneracy pressure. The cores of giant planets are dense enough that the electrons in the gas occupy about $h^3$ of phase space each. The Pauli exclusion principle means that they cannot all occupy low energy/momentum states. This means that even at relatively cool temperatures the gas can still exert considerable pressure due to the ...

11

Although we don't have a quantum theory of gravity, we think we have some reliable knowledge about the properties of black holes from general relativity. One thing we think we know is the so-called "No-hair conjecture", which says that black holes can be described by just three numbers: mass, charge, and angular momentum (i.e. how much they are spinning). ...

9

The image below represents the Sun's density gradient, which shows how the density changes with the radius. The ground we stand on should have a density between 2 to 3 $g/cm^{3}$. That should put you just above the water point on the vertical axis. The corresponding radius is then about 0.45 of the solar radius. Note that the vertical axis is in a ...

8

Whilst the question is I think largely a matter of conjecture, let me point out that matter exists in basically two phases inside a white dwarf. The outer part of a white dwarf is a gas, albeit a very dense one, consisting of a degenerate gas of electrons and a non-degenerate gas of completely ionised ions. The inner part can (if it has cooled sufficiently ...

7

Density is a 3-form, since you would write it as $$\omega:=\rho\text dx\wedge\text dy\wedge\text dz.$$ In special relativity it remains (the time component of) a 3-form. More specifically you have a current density $J$ of the form $$J = \rho\text dx\wedge\text dy\wedge\text dz + J_x \text dt\wedge\text dy\wedge\text dz+ J_y \text dx\wedge\text dt\wedge\text ... 6 It depends on how the quantity in question transforms. Almost always, densities in the form of "stuff per unit volume" and generally the "stuff" (like a charge) is a scalar (a number of things - number of elementary charges), but the volume it is contained in is observer dependent, owing to the Lorentz contraction. Therefore the density is ... 5 Sometimes I feel Wikipedia is a funny place... In the article you quote they provide a calculation from our patent application (see, e.g., http://akhmeteli.org/wp-content/uploads/2011/08/vacuum_balloons_cip.pdf ) proving that a homogeneous shell made of any existing material cannot be both light enough to float in air and strong enough to withstand ... 5 If we take neutron star material at say a density of \sim 10^{17} kg/m^{3} the neutrons have an internal kinetic energy density of 3 \times 10^{32} J/m^{3}. So even in a teaspoonful (say 5ml), there is 1.5\times10^{27} J of kinetic energy (more than the Sun emits in a second, or a billion or so atom bombs) and this will be released instantaneously. ... 4 This is because the whole boat, along with the air in the boat, is lighter than the water it displaces. For example, if a small boat will take up 1 cubic meter of water, then it has to be heavier than the weight of 1 cubic meter of water. This is explained in this post by What If here. For the same reason that bowling balls float (because salt water the ... 4 It is commonly believed that the speed of sound at high densities is bounded from above by c/\sqrt{3}, where c is the speed of light. Calculations of this quantity in many theories, ranging from QCD to systems with scale invariance, have all shown it to either stay below or exactly saturate the bound. See the introduction of this paper for a recent ... 4 It's true. Special equipment and a long time is required to mix helium and nitrogen. According to one study, a mixture of 2.7% He, 93.3% N at 800 p.s.i.g. required a special cradle to repeatedly upend the cylinder, and 20.5 hours to reach equilibrated gas, which then remained mixed: http://pubs.acs.org/doi/abs/10.1021/je60005a002. The helium repeatedly ... 3 The black hole event horizon is not a thing i.e. not a physical object. It is just a surface in spacetime from which light can never escape to infinity. Also, if we take the Schwarzschild description of a (non-rotating) black hole then it is a point mass hidden away behind the event horizon. You can't spaghettify a point mass. When two black holes merge, ... 3 I've just remembered that there was once a suggestion to use a mixture of xenon and oxygen under high pressure to allow people to float/fly/swim in it. It was also stated that water could be lighter than such a mixture. According to Smithsonian Physical Tables the critical point for xenon is 16.6\,\text{C}^{\circ},\quad ... 3 Your question states that We think we know that matter is anything having mass and that it occupies space but in fact, we know better than that. We have good reason to believe that fundamental particles are point-like. In other words, they have no internal structure, size, or volume. And they indeed have mass. We have a theoretical understanding (in ... 3 In the standard model of particle physics which fits the data up to now elementary particles entering the lagrangian are point particles with mass. The electron, for example is one of the elementary particles, and it does have a mass and the fit gives it 0 volume. There are experiments which try to set limits to how small the volume of the electron is. ... 3 The important thing about a density is that its integral over any volume, which represents the total charge (or whatever it is a density of) inside that volume, is finite. At r=0, \theta is not defined since the polar coordinate chart for \mathbb{R}^n covers everything but the origin. However, since the origin as a point is a set of zero Lebesgue ... 3 To derive the Bernoulli equation for inviscid fluids, the plan is to rewrite the Euler equation in such a way that we have gradients. I'll write the Euler equation with gravity here$$\frac{\partial \vec{u}}{\partial t} + \vec{u} \cdot \vec{\nabla} \vec{u} = -\frac{1}{\rho} \vec{\nabla} p + \vec{g}.$$Recall g = - \vec{\nabla} \Psi, and \vec{u} \cdot ... 3 Your intuition is right: the density of the string goes down a little bit when you increase the tension. HOWEVER: the wave in a string is a transverse wave which depends on the tension and the mass per unit length. If you double the tension the mass per unit length goes down by a small amount (the string gets a bit "thinner" because it gets longer) . Both ... 3 There is no relationship between the density of a metal and its electrical resistivity. There is a big database of material properties called MatWeb which is recommend as a legitimate source of data by UCSD's and Stanford's library systems, Rose-Hulman, etc. I took data from around 60 different metals and graphed them: As you can see there is no ... 3 Far away from a black hole, spacetime is curved only a little bit, and many different things could curve it like that out there. It's like if you had a dollar in your pocket, and it's been there for a long time, and you can't remember if you got it from your boss or from your friend. But a dollar is a dollar. So you could have a massive star, or a black ... 3 One should always specify whether one is talking about rest mass per unit rest frame volume, \rho_0 = m_0/V_0, rest mass per unit observer-frame volume, D = m_0/(V_0/\gamma) = \gamma\rho_0, or relativistic mass per unit observer-frame volume, (\gamma m_0)/(V_0/\gamma) = \gamma^2\rho_0.1 (I can't imagine the fourth case, relativistic mass per unit rest ... 2 So I am guessing you have a a 2 dimensional density? say, kg/m^2? In this case, you will need to get the area of your box -> say it is 2m^2. The mass of the box is 2 * 0.5 = 1 kg. But the mass of your person is 80kg. So your new mass is 81kg. This means the new density will be 81/2 = 40.5kg/m^2. The item will only float if the item has a lower density ... 2 I don't see how this can be done, given the problem as-stated. What defines it as being 2 superimposed sounds, rather than just 1 sound, other than just an arbitrary definition? What stops me coming along and saying: "No, it's actually 4 superimposed sounds, or 27!"? If both sounds are coming from the same source then any shift in speed or frequency of each ... 2 The density of a black hole is the mass divided by volume:$$ \rho=\frac M V=\frac M{4/3\pi R^3}=\frac{3M}{4\pi}\left(\frac{c^2}{2GM}\right)^3=\frac{3c^6}{32\pi G^3 M^2}\approx1.9\times10^{19}\text{ kg}/\text{m}^3\left(\frac{M_\odot}M\right)^2 $$This means that the average density of the black hole decreases as the mass increases! We can also solve for the ... 2 Consider this. I have an Earth-sized quantity of water that I throw into space. Naturally, it will assume the shape of a ball. Only if it is non-rotating and is not being influenced by a tidal field. So is there some sort of simple formula that ties these two properties together? Yes. It is called the equation of hydrostatic equlibrium.$$ ...

2

In a static situation, the water would have a larger density when it has a larger pressure, so you could sink until you reach a level where the density matches. In reality, the water can have a different temperature and a different salinity (both of which affect density) and if can be flowing (up/down, east/west, north/south) and so it might never settle ...

2

Your parameter $E$ is the bulk modulus, and this is a measure of how compressible the medium is. Easily compressible media like gases have a low value of $E$ while almost incompressible fluids like water have a very high value for $E$. Actually we should really use the symbol $K$ rather than $E$, because $E$ is normally used for the Young's modulus. And ...

2

The article you refer to is talking about the speed of sound (or speed of longitudinal wave vibrations) within a material and how that relates to volumetric mass density. If you were transmitting sound from one end of a guitar string to another, this would be relevant. But the sound produced from a string is not related to the speed that it travels within ...

2

If you have an object immersed in air, then you can calculate the forces on it using Archimedes' principle. There are two forces to consider. Firstly you have the weight of the object, which is simply: $$F_g = mg$$ where $m$ is the mass of the object and $g$ is the acceleration due to gravity. This force acts downwards. Secondly you have the bouyant ...

2

I will focus on just a little bit of one of your questions - the relationship between compressibility, density and pressure - and per my comment, recommend that you narrow down the scope of your question. As you know, in a gas we experience "pressure" because molecules hit the walls of the containing vessel. When I double the number of molecules in the same ...

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