Questions tagged [volume]

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Particle states per phase space volume of a quantum gas

Consider a quantum gas in a box with volume $V=L^3$ and temperature $T$, consisting of spinless bosons. Explain why the number $dN$ of "single-particle states" in a "momentum space volume" $d^3p$ is ...
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1answer
616 views

Invariant Phase space volume under canonical transfromation

I have a volume element in phase space: $$ d\omega = \prod _{i=1}^{N}(dq_{i},dp_{i})$$ Now I should show the invariance of this product under canonical transformations. I think first I would have to ...
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427 views

Simple gas in cylinder modeling

I want to do a simple (physically plausible but not physically accurate) simulation of a gas in a cylinder as it works on or is worked on by a piston. Wikipedia gives a good example of an adiabatic ...
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1answer
49 views

Calculating the compressed air by tides

I couldn't find any information on this topic. That is why I decided to ask in here. Can air be compressed by tides? I have an aquaponics setup next to the sea. When the high tide occurs, will you be ...
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45 views

Can you plot irreversible but quasi static processes on a $pV$ diagram?

I've often heard that you can't plot irreversible processes on a $pV$ diagram, but what about in the case where you have a quasi static process with friction? There still exists a curve of ...
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23 views

What Are The Physics and Air Pressure Effects of Extremely Large Bells

How would one go about figuring out the physical properties of when a bell is hit. Can I parameterize the diameter of the bell, its height, and the kinetic force of the knock to get the volume in ...
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1answer
31 views

Fluids mixture density prediction

As you know 100 ml of H2O mixed with 100 ml ethanol is not 200 ml What is the official name of this 'volume loss'? Is it possible, and if so, how, to calculate, before mixing, what the density of a ...
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31 views

Calculating infinitesimally small volume of a sphere in velocity space

This link (at the end of the page) is deriving the formula to calculate an infinitesimally small volume $dV$ on the surface of a sphere with radius $v$ in velocity space. It states that $dV = ...
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1answer
94 views

Relationship between volume and surface density

I was not sure if it fits better here, or in the math forum, but this is the problem I am trying to solve: Say you have a full cylinder of radius $R$, height $L$, and its uniformly charged with ...
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45 views

Distance Dependence of Van Der Waals Forces and his Equation of State

I've been trying to reconcile the form of the van der Waals equation of state and the equations from which they are derived. Stop me where I go wrong: The VDW EOS includes two terms: one for the ...
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2answers
202 views

Relation between surface area/shape and pressure

For a shape with a given volume and given gas pressure inside the volume, if the shape is changed to increase the surface area, will the internal gas pressure change?
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91 views

What is local volume fraction of material?

I'm reading a text on shape optimization by homogenization method. There the author describes that the composite structure resulting from the homogenization method is determined by two functions: $...
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1answer
110 views

What is the atomic composition of the human body, by volume?

According to Wikipedia, the composition (by atomic percent) of the human body is: 62% hydrogen 24% oxygen 12% carbon 1% nitrogen etc. Question: What is our volumetric composition*? *I get this is a ...
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53 views

Zero mean curvature and maximal volume

I have a 1+1 asympotically flat spacetime system (spherical symmetry) for which I'm trying to find the hypersurface which maximizes the volume enclosed in a sphere of a given radius $r=R$. **It seems ...
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621 views

Formula for residence time/turnover rate with unsteady state

I'm not sure this is the correct place to ask my question... but maybe someone could still help me. I'm looking for a way to calculate the residence time/turnover rate. I have the production and ...
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2answers
16 views

If gases are not ideal at high pressures, why doesn't raising the temperature of a gas make it less ideal?

I'm learning about ideal and non-ideal gas behavior in Chemistry, and my textbook and online sources say two things. 1) gases behave ideally at high temperatures and low pressures. 2) Gases behave non-...
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41 views

Density of States

For getting the density of states formula for photons, we simply multiply the density of states for atoms by 2 (due to two spins of photons). I am getting the 2D density of states formula as :- g(p)dp ...
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25 views

Phase transformation at constant volume $V$

A source heats water inside a vessel (V=constant). As soon as boiling begins, pressure raise up. How will the system evolve? Depends on the heat? How would be the relationship between the temperature ...
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9 views

Does multiple outlets (at same level on tank) from an overhead tank increase pressure?

I have a tank that is about 1foot high from my shower, however the pressure(or volume) isn't sufficient. Is it possible to increase the pressure(or volume) at the showerhead by doing the following: ...
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1answer
33 views

Why do some textbooks use $T$-$V$ diagram for temperature table instead of $p$-$V$ diagram?

I am confused about this thing. In the temperature table, the first column explains specific temperature and the second column explains corresponding saturation pressure. From what I understand, if ...
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22 views

Change in entropy due to the change in volume

If its given that $N$ no of Ideal gas atoms are in $V$ volume. What will be the change in entropy in units of $N\cdot kb\cdot\ln2$ when the volume is increased fourfold, i.e. $V \to 4V$, keeping ...
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37 views

Demonstration of comoving volume between 2 redshifts

1) I can't manage to find/justify the relation (1) below, from the common relation (2) of a volume. 2) It seems the variable r is actually the comoving distance and not comoving coordinates (with ...
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32 views

What is the volume inside the inner event horizon of a Kerr black hole?

(Dokuchaev 2011) found periodic orbits of particles and photons inside a Kerr-Newman black hole with a maximally extended global geometry. They orbit inside the inner horizon $r<r_-$ where the $r$ ...
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1answer
35 views

If water vapor changes its phase, how is it possible to maintain specific volume?

I was doing my thermal engineering exercises when I encountered a problem. The problem specified a fixed and rigid container with a volume $V=0.17\ m^3$, as I have a $T-S$ diagram for water, they give ...
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25 views

What is the volume of water in an inclined pipe

Diagram: I have a tank of water T, which was filled with 2000l of water. At some point along the pipe connected to it, there is a leak, which is leaking at the rate of 400l/24 hours. Valve d and j ...
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46 views

Thermodynamics, Phase change diagrammes

What would be the phenomena and PV, TV diagrammes for a closed vessel partially filled with water and subjected to heat, How change in vapour pressure would effect its boiling?, How PV, TV diagrammes ...
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35 views

How can I get the height that sits above the waterline of a partly-submerged object?

If I know the density of water (say 1024 kg/m^3) and the density of ice (say 900 kg/m^3), and the volume of an object (say 8 x 10^9 m^3), how can I figure out how much of it is sitting above or below ...
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1answer
104 views

What process is it when the polytropic index $n$ is equal to $- \infty$?

From $$Pv^n = \mathrm{constant}$$ When $n = - \infty$ What kind of process is it.... Eg... When $n= \infty$, It is constant volume.... Therefore when $n =- \infty$... What is constant?
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70 views

Volume expansion rate

In the paper Backreaction in late-time cosmology by Thomas Buchert and Syksy Rasanen, Annual Review of Nuclear and Particle Science 62 (2012) 57-79, in eq .2.2 the covariant divergence: $$\nabla_\...
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1answer
64 views

Two containers that have the same volume (let say 500 liter) but are different in shape

I remember from school, one time a teacher explain us the following: two containers of the same volume, but one is thin and tall, and the second is short and wide. then if we fill them with water from ...
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45 views

Volume within equi-energetic surface of a classical harmonic oscillator in microcanonical ensemble

$$ V(E) = \int_{H\leq E} d\mu = \int_\Gamma d\mu\, \Theta\bigl(E-H(q,p)\bigr) . $$ To compute the volume within the equinergetic surface in the microcanonical ensamble, we use the formula above, ...
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34 views

Determining pressure as a function of time for water filled balloon

Looking to determine pressure as a function of time for a water filled "balloon" at extremely high pressures (~90MPa) with a fixed flow rate out. This is to determine the time it takes to hit a ...
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1answer
89 views

PV diagram of pure substance

Why does the specific volume of saturated solid state of water decreases with increasing pressure and the specific volume of saturated liquid wrt vaporisation increases with pressure? Can anyone ...
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1answer
37 views

Limit charge of electronic–hydraulic analogy of a compartment

I am doing a mathematical model of an hydraulic system and I am using an electronic-hydraulic analogy. Normally a compartment is simulated with a capacitor. But in my system I can apply a big ...
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1answer
279 views

Density function in phase space

What does density function in phase space physically mean? How does it indicate, the more familiar density that we are accustomed to ( an analogy may be), in phase space?
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73 views

How can I know the volume occupied by one element in a compound?

I struggle to find how to estimate the volume occupied by one atom in a compound. As an example let's take $\beta$-Ga$_2$O$_3$, since that's the material on which I work the most. The crystal ...
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1answer
577 views

Phase space volume doesn't change under canonical transform

I have given a set of generalized coordinates $(q_1,..q_n,p_1,..p_n)$. Suppose I had a canonical transform $(q_i,p_i)\rightarrow (Q_i,P_i).$ I am trying to show that the phase space volume element ...
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1answer
222 views

Inmersion of homogeneous straight cone into a liquid

I have a problem with an exercise that I require help: Find the immersion of a homogeneous straight cone of height h and specific weight $\gamma_1$ in a liquid with specific weight $\gamma$. The ...
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1answer
51 views

In which dimension should nearest neighbor distances be calculated? Confusion regarding some concepts

In this paper, Abstract—The intrinsic dimensionality of a set of patterns is important in determining an appropriate number of features for representing the data and whether a reasonable two- or ...
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2answers
85 views

How much water is transported as a shallow water wave travels into a sea cave?

How much water is transported (volume) as a wave travels into a sea cave? The wave has a height of 1m and a period of 12 seconds. The average water depth at the cave mouth it 5M and the width is 15m....
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76 views

Volume of cubes thrown in a container

I am trying to calculate how many lego bricks I can fit in containers of a given sizes. Basic 1x1 lego brick is 8 x 8 x 9.4 mm so it has a volume of ~600 mm² Then we have a container of size 192 x ...
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1answer
273 views

Energy density of a 0D point particle vs. a 1D string

As I understand there is a problem in physics where point-like massive (or charged, etc.) particles would have infinite mass/energy (or charge, etc.) density. I'm curious how in the context of String ...
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2answers
84 views

Dimensional equation for measuring logarithm of volume

I have a measure that uses radiation dose (M.U. $Gray$) and $\log(Volume)$. The measure is $[\frac{Dose}{\log(Volume)}]$ that is $[\frac{D}{\log(l^3)}]$ with $D$ as radiation dose (M.U. unit is Gray) ...
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1answer
62 views

Investigating volume of a crater

I determined the shape of the crater to be a spherical cap. According to this website, http://mathforum.org/library/drmath/view/55253.html , its formula is described as $$V_{cap} = \frac{1}{6} \pi h (...
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1answer
51 views

Construct bivariate symmetric (polynomial) Hilbert-Schmidt two-qubit volume functions over the unit square with certain properties

Construct bivariate symmetric polynomials (two-qubit volume functions) f(r,R) = f(R,r) >= 0 over [0,1]^2, with f(1,R) = f(r,1)=0, such that the univariate marginal (integrating over r or R) ...
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48 views

Help with vacuums?

Okay, here is my understanding. Please correct me if anything here is incorrect. Suppose I have a cube with a side length of ten inches. It has a surface area of 600 square inches, and at an ...
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1answer
57 views

Can volume be interpreted as density $\times$ volume?

In this optimization presentation there's a "volume constraint": $$\sum_{i=1}^{n_{el}} v_i p_i \le V^*$$ where $v_i$ is the volume of a node element and $p_i$ is its density. But because $density \...
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2answers
882 views

Multidimensional Area and Volume

In 3D the volume is $xyz$, the product of three coordinates. But in $N$ dimension ,how to define area and volume?