Questions tagged [volume]

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222 questions
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Did the Chernobyl power station's water cistern really hold $7000\:\rm m^3$? [closed]

In he HBO TV miniseries Chernobyl, they talk about a cistern holding 7000 cubic meters of water. That is the content of Loch Ness, the deepest lake in the UK. Would the Chernobyl reactor really hold ...
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Counting unitary transformations in $SU(N)$ [migrated]

I'm referring to the following article 1, in particular to section 6. The goal is to estimate the number of unitary transformations in $SU(N)$, identifying unitaries within balls of radius $\epsilon$....
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What happens to temperature as volume increases (charles law)

Let us take Boyles law to start. Assumptions: Gas is perfect. In a massless piston that can be expanded with no friction Adiabatic If we were to decrease the volume of the piston, the pressure ...
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How can internal energy be expressed as a function of any two of $p, v, T$?

In the book of Irey, Theormodynamics, the author states that (while talking about single phase substances) For a simple compressible media, we may choose our measurable independent variables any ...
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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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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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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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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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Does the total energy in a volume (gas) increase linearly with increases in pressure?

If a volume has a certain pressure, then double that pressure at another time, is the total energy stored doubled? I'm sure this has to do with thermodynamics and if I remember correctly there is a ...
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Volume of hypothetical closed universe

Consider a physical universe with a beginning in time and space, with a finite amount of mass without the complications of dark energy that we have in the presently open curvature universe, so that ...
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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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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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How is a helium tank volume measured?

I'm comparing different helium tank offers and I found an interesting one which seems to be what I want, but I'm unsure regarding the volume. It states: The content of gas of this tank is greater ...
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Definition of volume of a gas and Amagat's law

How would you define the volume of an (ideal) gas? I would say it is the volume of the container holding the gas (whether it is a fixed container or a flexible one like a balloon). However, ...
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What is the physical meaning of divergence? [duplicate]

I want to visualize the concept of divergence of a vector field. I also have searched the web.Some says it is 1.the amount of flux per unit volume in a region around some point 2.Divergence of ...