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 ...
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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{\...
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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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Volume element in system phase space

Consider $N$ particles in $3D$, with coordinates $q_i$ and momenta $p_i$, so $\{q_1,p_1,q_2,p_2,...,q_{3N},p_{3N}\}$ are variables. Construct a phase space of the system, with axes $(q_1,p_1,q_2,p_2,.....
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What is the general dependence of volume change from mass change due to general relativity?

The volume excess of earth due to general relativity in comparison to euclidean space has been calculated to $$ \Delta V = \frac{ G M \pi R^2}{5 c^2} = 113 km^3 $$ (this is done in this physics....
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An ideal gas expands into vacuum in an insulated rigid vessel. Which of the followings happens? [closed]

This question came in the Dhaka university admission exam 2018-19. An ideal gas expands into vacuum in an insulated rigid vessel. Which of the following happens? A. no change of internal energy B. a ...
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Enthalpy, why is work only partially done?

If a system with const. pressure can change it's volume free, a heat transfer into the System results in a partial work done, which gives back the inner energy addet partial back to the environment. (...
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Is there a temperature difference when I change the volume instantaneously? [duplicate]

If I were to instantaneously remove the wall as drawn above, then there is no loss of molecular velocities --> T1 = T2. But I have a problem imagining that there really is no change in temperature. ...
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Can we have constant volume, and pressure in a system?

I was given a system where heat was added to a mass of Nitrogen gas in a canister at constant pressure? And given the volume of the canister as 1L, I assumed that the gas would expand to fill the ...
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Square of Volume of Tetrahedron in Loop Quantum Gravity

In the subsequent statement about the geometry of Tetrahedron in Carlo Rovelli's book, there is a formula as follows: $$V^2 = \frac {2}{9}(\vec L_1 \times \vec L_2)\cdot \vec L_3$$ Where $\vec L_a$ is ...
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Density reduction in a two component object [closed]

I have a metal object with a mass of 1.374 g, a Volume of 0.315 cm3, and a density of 4.362 g/cm3. I have a buoyant material with a density of 0.609 g/cm3. How do I calculate the amount of buoyant ...
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Understanding the shape of Carnot loop in the $p$-$V$ plane

The area enclosed by a loop is the total work done. If you draw a square, isn't that the maximum amount of work done possible instead. Why is the isothermal/adiabatic path the most efficient instead ...
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What are the surfaces that contain an interior volume (space separating) called? Are they related to orientability?

I know that a "closed" surface is defined as a compact surface with no boundary. I don't have it clear if they have something to do with having an interior volume (completely enclosed volume)...
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Free particle in momentum representation

In Greiner, density operator for a free particle has been calculated in momentum basis. They consider a large box of vilume $V=L^3$ and periodic boundary condition. $$\phi_\vec{k}(\vec r)=\frac{1}{\...
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Van der waals equation why should we divide excluded volume by 2?

So been looking at the correction term $b$ for the Van Der Waals equation. I understand that we look for the excluded volume. I see it as the volume where no (center of a) particle can enter. We start ...
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Two Liouville's theorem

Within the context of Hamiltonian mechanics and phase spaces I have learnt that the phase space distribution function is constant, in other words, that the "volume" of any region is constant,...
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Derivative of Energy wrt Volume Expectation

Small problem that has been bugging me for a while and I can't seem to demonstrate the validity of $(4)$ below. Starting with enthalpy, $$H(S,P)-U(S,V)=PV$$ Recognizing the Legendre transform here, $$\...
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Definition of a point in physics [closed]

What exactly is a point in physics? I understand that in geometry this is unambiguous, but how does it relate to the real world? Is a point particle an object? Is a point in space a volume in space? ...
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In Griffiths' Electrodynamics, how does he calculate the contribution of two opposing faces of infinitesimal rectangular volume to a surface integral?

In appendix A of Griffiths' Electrodynamics, he sketches proofs of certain theorems of vector calculus. My question is related to this question, indeed the latter concerns the exact passage of the ...
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Extracting useful energy inline to a pressure relief valve?

So imagine if we have a pressure vessel being pressured with a pump. Let's say there is a pressure relief valve that's necessary in the design. Would you actually be able to extract useful work from ...
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1 vote
1 answer
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QFT for an extended electron

Has somebody already formulated a QFT (e.g. QED) for an extended electron (e.g. as a spherical charge) such that the point particle limit gives the usual QFT? Is anything know about the connection of ...
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Question about volume of water [closed]

As shown in the figure, the lead straight cross-section of a reservoir and two mountains is shown. The rectangular groove at the bottom represents the reservoir, and the isosceles triangle on both ...
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Non-Ideal Gas Question

I have been attempting to solve a problem involving a non-ideal gas. The gas is assumed to be non-ideal and hence modelled by the Van der Waals Equation, it is considered to be pure hydrogen gas and ...
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Why temperature increases with increase in volume?

If We heat an ideal gas, its temperature rises and it's molecule becomes energetic hence they move more and more away from equilibrium position. But when we increse the volume of gas , why does its ...
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3 votes
2 answers
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Properties of the "volume element" in momentum space in relativity

I am reading Landau's The Classical Theory of Fields. On page 30, section 10, the last paragraph reads: To solve the problem, we first determine the properties of the "volume element" $...
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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?...
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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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How to deal with cubic terms in Gibbs free energy?

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 = \...
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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 ...
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-1 votes
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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3 votes
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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 ...
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Is there a formula for volume in a open universe?

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 ...
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Problem on Archimedes' principle [closed]

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 ($\rho_m$= ...
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