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2answers
30 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
44 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 ...
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votes
1answer
25 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
932 views

Find the center of mass of a hemispherical shell

Problem: Find the center of mass of a hemispherical shell of constant density and inner radius r1 and outer radius r2. Attempt at Solution: Let the hemisphere be in the region $z>0$. By symmetry, ...
2
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0answers
157 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 ...
1
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0answers
29 views

Volume Operator / volume phase-space-function in thermodynamics

In Thermodynamics, one often encounters the derivation of pressure as the generalised force that belongs to the extensive state-variable of the volume. Postulates: One looks just at a system of many ...
1
vote
0answers
55 views

Is $d^3r$ the same as $dV$, the volume element?

I've seen the term $d^3r$ being used instead of $dV$. Are they exactly the same? Do they have a different connotation?
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0answers
33 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 ...
1
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0answers
276 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 ...
0
votes
0answers
22 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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votes
0answers
19 views

How can I estimate the density of non-ideal vapor mixtures

I am trying to estimate the density of a non-ideal gas mixture and can't seem to find any resources for how to go about this. For some gas pairs like ammonia-water there are empirical correlations ...
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0answers
81 views

Is Isochoric compression or expansion possible?

Stirling cycle is made of two isothermal and two isochoric processes. Heat is added isothermally, expansion and compression takes place isochorically, as given by the book. How can a gas be ...
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0answers
52 views

What happens when electromagnetically shunken coin is heated

The question is simple: What happens to coin/object that was electromagnetically shrunken by a coin crusher device is then heated until it (I asume) melts? Do I have misconception or not just ...
0
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0answers
42 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 ...