# Questions tagged [volume]

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### Meaning of Einstein's condition on the metric tensor

Quote from Nothing but coincidences: the point-coincidence and Einstein’s struggle with the meaning of coordinates in physics by Marco Giovanelli: On November 11, 1915, Einstein returned to a set of ...
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### Sethna 3.2.1 - What does it mean to integrate over configuration space?

I'm having trouble understanding the examples Sethna uses in this section to illustrate the microcanonical ensemble. First he talks about the probability density $\rho(Q)$ that $N$ ideal gas particles ...
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### How to measure cylinder volume by water weight

I'm trying to determine the volume of a cylinder ( 25 cc approximately) in a precise way. First I'm measure the weight of the empty cylinder. Then, I'm add water to the cylinder until the water ...
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### Determining the Number of Points in the $n$-Space

Electron gas is a collection of non-interacting electrons. If these electrons are confined to certain volume (for example, cube of metal), their behavior can be described by the wavefunction which is ...
1 vote
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### Calculating proper volume in the Alcubierre spacetime

I'm trying to calculate the proper volume of a portion of the alcubierre spacetime to see how it compares to the euclidean volume element. As I understand it, the proper volume element in cartesian ...
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### Pressure / force: surface vs volume

I recently read about measuring the expansion of wood when wet. The set-up (A) was a 1" cube of wood, in water, with a load sensor above, which reported ~100 lb/in^2 (I think they meant psi). I ...
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### Is a path integral over a region with a bottleneck still unitary?

Consider the following hourglass-shaped region of spacetime: The red circular cross sections are the initial and final conditions, which can vary, while we fix a particular boundary condition on the ...
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### Why is bulk modulus positive in equilibrium?

$B=-PV/\Delta V$ The negative sign indicates that when pressure increases, the volume decreases. That is, if $P$ is positive, $\Delta V$ is negative. Thus for a system in equilibrium, the value of ...
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### How to derive $TV^{1-\gamma}$? I get $\frac{T}{V^{1-\gamma}}$ [closed]

For an adiabatic process we have $dQ=0$, thus the first law gives: \begin{align} \mathrm{d}E &= \mathrm{d}W, \\ nC_V \mathrm{d}T &= - P\mathrm{d}V = - \frac{nRT}{V} \mathrm{d}V, \\ \frac{\...
1 vote
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### Rankine Cycle $pV$ diagram

I was going through the $pV$ diagram of the ideal Rankine cycle and all of the images that I found on the internet and as opposed to the $TS$ Diagram, they tend to show the compression in the ...
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### How comes, that my book states that internal energy is dependent on volume?

Currently I am reading in the 11 edition of Physical Chemistry, Atkins in the chapter 1st law of thermodynamics. A few pages ago I learned the following: Makes sense for now, as far as I know it ...
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### On the Sum of Collisions from each coordinate

I was self-reading the gas laws stuff in this book at page $18$. In chapter two author tends to derive the formula for, $$\ P=\frac{2K.E}{3V}$$ Where $P$ is pressure and $K.E$ is kinetic energy and $V$...
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### How is Avogadro's law tested practically?

I was reading about Avogadro's law which states that Equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules. My question is, how can one ...
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### Mass and Volume increase

Under relativity, does the mass AND volume of a body increase with increasing speed, or is it just the mass increasing. as in "getting denser"? My apologies, if this is a trivial question.......
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### Why do we need to consider the area under Volume axis to find the work done by a gas?

For a $P$ vs $V$ graph for gas, why do we need to consider the area under the volume axis for determining the work done by the gas? Can't we take the area under the pressure axis to find the work done?...
1 vote
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### In reversible process, why define $\delta W=-PdV$ instead of $\delta W=-VdP$?

For a reversible process, it is assumed that the external pressure $P_{ext}$ is infinitesimally different from internal pressure $P_{int}$. So in reversible process, I can have $~P_{int}=P(V,T)~$ but ...
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### Volume and density estimates for electrons in outer space (near 2.9 Kelvin temperature)

Assuming the mass of an electron is contained in a volume greater than zero (and thus NOT a point mass), what is (are) the measured and/or calculated density (or density ranges) of an electron? How ...
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Consider as a toy example a system with Gibbs free energy given by $$G(p,T) = p^3 - 2p^2 - p + 2.$$ If I was to find the Helmholtz free energy, I would try Legendre transforming $F = G - pV$, $$V = \... -3 votes 1 answer 169 views ### Why aren't liters a SI Unit? And why isn't there a unit for volume? In the International System of Units, there is the second for time, the metre for length, the kilogram for mass, the ampere for electric current, the kelvin for temperature, the mole for density, and ... -1 votes 2 answers 36 views ### Frequency and Volume Relational in Sound In a real life example: Suppose if I change the volume of TV, Computer or, Stereo sound device, would the frequency of sound change as well? In other words, when I lower the volume does it make ... 0 votes 2 answers 60 views ### Volume in spherical units (I asked this questions in Mathematics section but there were no answers.) I'm working on Cavendish's original analysis of his experiment. Cavendish does not use equations or standard units. For ... 0 votes 2 answers 212 views ### What is the general formula of work in terms of pressure and volume? I've seen work often represented by the formula$$W = PΔV$$But there are also other formulas, which represent different types of work. For example, Non Flow Work$$ W =\int_{1}^{2} PdV $$Steady ... 0 votes 1 answer 122 views ### Volume element of manifolds via wedge products I'm following Carroll's book on General Relativity and in chapter 2, section 2.10, he claims that the volume element can be identified with$$d^nx=dx^0\wedge\ldots \wedge dx^{n-1}.$$I understand why ... 0 votes 0 answers 4 views ### Will two spherical fluorescent particles have a lower fluorescence. When compared to one spherical fluorescent particle with the same volume? So image you have two groups one group consist out of 1 fluorescent particle and the other group consist out of multiple particles. However, the volume of the particles combined is the same for both ... 2 votes 2 answers 75 views ### Flattening a sealed bag in space Let's say you're in space, and you have an empty, sealed, round bag in space (full of "nothing" since there's no air). Is it possible to flatten the bag without unsealing it? My ... 3 votes 1 answer 342 views ### How do we calculate a volume in curved space? The volume of a sphere in flat space is:$$V = \frac{4}{3}\pi r^3.$$In curved space, r itself is dependent on position, so, in spherical coordinates,$$r=r(r, \phi, \theta) . Assuming a spherical ...
Recently while reading a bit about cosmology, I have stumbled upon two different formulas that describe the full volume of a universe with its spatial section $dt=0$. For instance, for a flat universe ...
I have to solve the following problem about the Archimedes' principle. Let a cubic block of iron ($\rho_i$ = 7860 $kg / m^3$ ) side 10.0 cm ($l_{cube}$) was placed in a tub of mercury ($\rho_m$= ...