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2
votes
1answer
53 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 ...
2
votes
2answers
295 views

Relationship of the volume of a plumbing system to pressure

How does the volume of water a plumbing system holds vary with water pressure? I know the ratio would include the modulus of elasticity of the plumbing material, the total surface area of the plumbing ...
2
votes
7answers
29k views

Water pressure calculation for a volume of water at a given height

I'm looking to create a rain harvesting system. I have a 275 gallon IBC tote that is 48" x 40" x 46". I have an adapter for a 3/4 garden hose at the bottom of the IBC tote. I'm trying to figure out ...
3
votes
1answer
35 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 ...
-5
votes
0answers
37 views

What is the volume of a 4d sphere [migrated]

What is the volume of a 4d sphere? I've seen so many site that would have answered this question, but all of them have so many numbers that some people (including me) don't understand. So I was hoping ...
0
votes
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
0answers
39 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?
0
votes
3answers
953 views

When Sugar Is Added to Water, How Does the Mass Change, and How does That Affect the Water's Density and Boiling Point?

I can't find a good answer anywhere. How does the amount of sugar added change the boiling point, mass, and density of water? Does it affect the mass or the volume? Or both?
0
votes
3answers
2k views

Specific heat capacity at constant volume VS constant pressure

For an ideal gas, why is the specific heat capacity at constant volume lower than the specific heat capacity at constant pressure?
1
vote
4answers
5k views

Surface Area: Volume and its relation with heat

In biology, it is stated that more surface area and less volume helps for keeping bodies cool. How can one explain this phenomena in terms of physics?
1
vote
4answers
5k views

Why does squeezing a water bottle make the water come out?

This seems natural, but I can't wrap my head around it when I think about it. When I squeeze an open bottle filled with water, the water will spill out. When I squeeze a bottle, the material ...
0
votes
0answers
22 views

Pressure in a balloon as a function of its diameter [duplicate]

Premise #1: Balloon is a perfect sphere Premise #2: We add water in order to increase the diameter of the balloon Is there an equation allowing us to find the pressure in the balloon, as the diameter ...
0
votes
1answer
90 views

What does Liouville's Theorem actually mean?

Basically, the mathematical statement of Liouville's theorem is: $$\frac{\partial \rho }{\partial t}= -\sum_{i}\left(\frac{\partial \rho}{\partial q_i}\,\dot{q_i}+\frac{\partial\rho}{\partial p_i}\,\...
0
votes
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 ...
6
votes
1answer
77 views

How do pressured containers within pressured containers behave?

If a container could hold 60 PSI of pressure and was placed into a larger container with the same strength, could you fill the large container to 50 psi and the smaller one to 100 psi, creating only ...
1
vote
2answers
44 views

Work applied to a thermodynamic system

What are some examples of a thermodynamic system where no work is done on the system, but the first law is applied? Work in thermodynamics is based around volume. Would that mean if the system's ...
4
votes
3answers
724 views

Why Liouville's theorem is obvious?

In Florian Scheck's Mechanics, he stated the local form of Liouville's theorem as follows: Let $\Phi_{t,s}(x)$ be the flow of the differential equation $$-J\frac{d}{dt}x=H_{x}.$$ Then for all $x,t,s$ ...
0
votes
2answers
65 views

Confused about volume, density and mass, help!

I got into an argument with my friend, which cast confusion on my understanding of density and its relationship to volume. I'm hoping to get some clarity. The argument involved describing density in ...
0
votes
2answers
67 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 ...
1
vote
0answers
34 views

Divergence theorem for cylindrical coordinates [closed]

I have a Vector field in a cylinder where x^2+y^2=4 and goes from z=0 to z=3 and a vector field A=(4x)i-(2y^2)j+(z^2)k and I'm trying to verify the divergence theorem for the vector field i set set ...
1
vote
3answers
35k views

Thermodynamics - Sign convention

I use the sign convention: Heat absorbed by the system = $q+$ (positive) Heat evolved by the system = $q-$ (negative) Work done on the system = $w +$ (positive) Work done by the system = $w -$ (...
1
vote
3answers
2k views

Why is density an intensive property?

I am still trying to understand what are intensive and extensive properties. Possibly someone can give a pointer to a decent text (preferably on the web), as I am not too happy (to say the least) with ...
3
votes
2answers
74 views

Why do some materials shrink when their temperature increases?

In my vision it would seem quite logical that all materials expand when temperature rises. Because the particles get more energy and travel larger distances when moving. But apparently there are ...
0
votes
1answer
49 views

Understanding the relation between pressure, ideal gas and, volume

I was given the following formula which is used for ideal gasses: $$pV = nRT$$ where: p:pressure V: volume n: number of moles R: gasconstant T: temperature now when speaking about vaporpressure ...
0
votes
1answer
136 views

How to measure the mass of the lower part of a human body?

An Olympic weightlifter asked me this question and it has been bugging me for a couple of days now. Suppose "lower part" is defined as anything below and including the hip. This means that the ...
0
votes
1answer
54 views

Precision of the edge of a cube versus the volume of a cube [closed]

The edge of a cube was measured with 1% precision. How is the precision of the volume of same cube calculated on the basis this measurement? Is it true that precision of the measurement would be 3%?
0
votes
1answer
35 views

Understanding why 2*density of a isolated gas equals half the initial temperature

A vertical cylinder of cross-sectional area 0.050 m2 is fitted with a tight-fitting, frictionless piston of mass 5.00 kg. The cylinder contains 3.00 mol of an ideal gas at 227°C. At what temperature ...
0
votes
1answer
49 views

Why divide surface area to volume for strength in living beings? [duplicate]

As the title says, why divide surface area to volume for strength in living beings ? I mean why all surface area ? Shouldn't it be area touching the ground ? Thanks in advance! :)
-1
votes
1answer
168 views

how to calculate diameter and length change from volume change for a hollow cylinder?

I have a cylindrical material with a hole going through its center all along the larger dimension (length). I know the dimensions and the volume of the cylinder at temperature T1. Now, if I heat it up ...
2
votes
1answer
86 views

Does limiting to infinity violate laws of physics?

It is noteworthy that one cannot simply divide any length more than the Planck-length. If so, one cannot simply divide any volume more than the $(Planck-length)^3$. So if I want to find the limit of ...
0
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) ...
1
vote
2answers
407 views

Volume of Brillouin zone is the same as Fourier primitive cell?

In Kittel's solid state text, problem 2.3, he says that the volume of the Brillouin zone is the same as a primitive parallelepiped in Fourier space. Somehow I can't see why this is true. Can someone ...
1
vote
1answer
327 views

Pressure Calculation - Compressed Air Volume [closed]

I am trying to calculate the change in pressure in a closed pressure vessel that is being compressed. For the sake of simplicity we can consider this to be a syringe with a closed end that is being ...
0
votes
1answer
70 views

why is air pressure in force per area instead of volume?

The basic unit of Pascals, (Pa), is one Newton (N) per meter square (area). Why is this, especially for things like air pressure that deal with three dimensional space? Shouldn't something like air ...
3
votes
3answers
964 views

Problem in understanding the Proof of $PV^{\gamma}$ =constant in thermodynamics

I have looked at the proof of this relation $PV^\gamma = C$; (where $P$ is pressure and $V$ is volume) in quite some places but I am not able to understand the logic behind the third step. In ...
1
vote
0answers
81 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
1answer
1k views

How do I keep the temperature constant in a Boyle's Law experiment?

I'm trying to get a head start on our lab experiment next week about Boyle's Law. The set-up is we have an air chamber can immersed in a pot of boiling water (which is kept boiling over an electric ...
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
vote
5answers
1k views

Is it possible for an object to have mass but zero volume?

Can there exist a particle/object in the universe having mass but no volume? Is it possible that mass can exist without volume and density? We think we know that matter is anything having mass and ...
0
votes
2answers
577 views

Point masses and infinite densities

Point masses are masses who don't have volume. It is said that they are infinitly dense, but I though division by zero is undefined hence you can't define the density for a point mass because $\rho=m/...
1
vote
1answer
49 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
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) ...
-2
votes
1answer
117 views
1
vote
2answers
3k views

Pressure vs Volume Calculation for air [closed]

I have 1 litre of air in a sealed container at atmosphere pressure (approx 15 psi absolute). I want to reduce pressure in the container by 1 psi ( 14 psi absolute or -1 psig). If I understand ...
0
votes
0answers
24 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 ...
2
votes
3answers
268 views

Would a person gain or lose weight after expelling a flatus?

Considering the chemical composition, mass, and pressure range of typical human flatulence, would a person gain or lose weight after passing gas?
0
votes
2answers
354 views

Calculate volume of a crater

Is there an equation I can use to determine the volume of a crater in my 'drop the ball on sand' experiment? I looked at the equations for volume of hemisphere and cone but do not seem to fit the ...
0
votes
1answer
73 views

Question about pistons and how their volume is affected by particles?

I can't find an answer to this anywhere. When pressure is maintained in a piston and an ideal gas is injected into it (again, with no change in pressure as it is injected) the piston is displaced ...
0
votes
0answers
116 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 ...
2
votes
2answers
106 views

Why is the introduction of a quantization volume necessary for quantization of the EM field

I have been working through the quantization of the electromagnetic field, and every source I find introduces a quantization volume with periodic boundary conditions in the process, in which we fit ...