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Questions tagged [volume]

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248 views

Virial expansion in terms of pressure

I'm studying thermodynamics and I found two forms for the virial expansion: $$pV~=~RT[1+\frac{A_2}{V}+\frac{A_3}{V^2}+\ldots] \tag{1}$$ and $$pV~=~RT[1+B_2p+B_3p^2+\ldots]\tag{2}$$ my problem is that ...
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81 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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153 views

What VOLUME does exactly the $V$ term in ideal gas equation represent?

According to kinetic theory of gases 'the actual volume occupied by the gas molecules are negligible in comparison to the volume of the container.' I believe that this assumption is significant ...
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74 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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580 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?
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1answer
95 views

Is the system derivative for mass, in the Reynolds transport theorem for mass, always zero?

The Reynolds transport theorem for mass is $$\frac{dm_{sys}}{dt} = \frac{dm_{cv}}{dt} - \dot{m_{in}} + \dot{m_{out}}$$ My question is the term $\frac{dm_{sys}}{dt}$ always zero. Since this is the ...
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1answer
35 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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1answer
96 views

Difference between p-v and pressure and specific volume

what is the difference between pressure-volume and pressure-specific volume curves? since volume is an extensive property why do we plot pressure and volume curves for different processes?
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1answer
301 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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1answer
96 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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1answer
51 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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28 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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1answer
52 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
29 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
164 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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1answer
347 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
112 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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1answer
148 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
46 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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1answer
55 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
47 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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1answer
53 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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0answers
415 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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0answers
35 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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0answers
81 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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0answers
50 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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0answers
600 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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0answers
44 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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25 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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61 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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28 views

Is there an influence of the air humidity on the air expansion by a temperature change?

I have found the following formula to calculate the expansion of air by a temperature change, if the pressure stays at the same level: ΔV = ​ɣ * V0 * ΔT This would give me an expansion of 46.96m3 in ...
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34 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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27 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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18 views

Volume in first octant

Here we are finding number of state less than energy E for particle trapped in 3D harmonic potential .For large value of E as compare to hw , we assumed energy levels as continuous.And we introduces ...
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13 views

Does magnetostriction change volume?

Does magnetostrictive material like terfenol D change volume,or does it just increase in one dimension and decrease in another keeping the volume constant?
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34 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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68 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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47 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 ...