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2answers
61 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 ...
0
votes
2answers
77 views

Pressure Volume graphs and work done

So if I have a system where pressure, volume, and temperature change, how do I find the work done on the system? I look at an example where you simply use $\mathrm{d}W =-p\, \mathrm{d}V$, but I ...
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votes
2answers
33 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) ...
3
votes
1answer
38 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 ...
1
vote
1answer
50 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 ...
0
votes
1answer
32 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 (...
-1
votes
1answer
2k 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
votes
0answers
178 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
vote
0answers
87 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?
1
vote
0answers
34 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
vote
0answers
318 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
42 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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0answers
18 views

Rate of Temperature Change in Air to Air Contact

What is the rate of temperature change when it is x Liters of air to x Liters of air at two different temperatures directly contacting each other? I need to know this for a hypothetical telekinesis ...
0
votes
0answers
23 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) ...
0
votes
0answers
28 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 ...
0
votes
0answers
56 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
votes
0answers
43 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 ...