Questions tagged [volume]

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1answer
83 views

Can the volume fix the thermodynamic state of a system?

Can we use the volume to fix the thermodynamic state of a system? If not, why do we use P-V curves to know about thermodynamic states and processes?
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1answer
115 views

Why the volume of a region is not a diffeomorphism invariant? (LQG)

In loop quantum gravity, the volume operator for a given region is not a diffeomorphism invariant. But classically we know that volume is a scalar quantity under a diffeomorphism even if we take the ...
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4answers
75 views

Does the pressure-volume-temperature realation of gases also work on solids?

I've read about the Combined gas law which said: The ratio between the pressure-volume product and the temperature of a system remains constant. My question is: Does this law also works on ...
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1answer
31 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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2answers
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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1answer
245 views

Why we can't multiply two extensive quantities together?

I have read that regarding the equation of state $PV=nRT$, since $V$ is an extensive quantity $P$ should be an intensive one because the product of extensive quantities is inherently non-linear. ...
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1answer
166 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
480 views

Calculating work done by a gas fitted with a spring

Assume a gas in a container with one end closed and other end has a piston of mass m fixed with a spring.The gas is then heated ,assume that the container is non-conducting.(Assume vessel to be kept ...
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0answers
35 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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1answer
349 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
302 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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2answers
859 views

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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1answer
60 views

Do indicator/p-V diagrams only show reversible processes?

In Equilibrium Thermodynamics, Adkins, it is stated that Since equilibrium state corresponds to definite values of the system parameters, we may represent a quasistatic process by plotting...an ...
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1answer
75 views

What part of the cylinder displaces some volume from the second liquid (which is used for the buoyant force)? [duplicate]

Consider a container filled with two liquids, of densities $\rho_1$ and $\rho_2$, such that $\rho_2 < \rho_1$. Now imagine placing a cylinder with the top base removed, of density $\rho,\space \...
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1answer
433 views

Andrew's experiments on CO2

While studying andrew's experiment on CO2 i found a contradictory thing to my knowledge. At isothermal temperature 13.1°c as pressure increases volume decrease. At a particular pressure CO2 starts ...
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1answer
89 views

Why can the equation of adiabatic process $P_1 V_1^\gamma=P_2 V_2^\gamma$ be written as $\Delta P/P=-\gamma \Delta V/V$?

Why can the equation of adiabatic process $P_1 V_1^\gamma=P_2 V_2^\gamma$ be written as $$\frac{\Delta P}{P}=-\gamma \frac{\Delta V}{V},$$ where $P_2-\Delta P=P_1$ and $V_2+\Delta V=V_1$ as in ...
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4answers
10k views

Is it theoretically possible to have a larger inside volume than the outside exterior?

Last night I was listening to the audiobook of Harry Potter and the Chamber of Secrets (yeah, I know..) and it talked about the trunk of their enhanced car that was much bigger from the inside, than ...
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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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2answers
129 views

Liouville Theorem analogue in generalized velocities?

The Liouville Theorem concerns dynamics in phase space: does an analogue exist in configuration space, and, if not, could you give a motivation / proof why?
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1answer
56 views

Can't understand how flow work is possible in a control volume

I am struggling to fully grasp the concept of flow work for a non-deformabable control volume. Nearly every source puts it in this way: flow work is the work required to push fluid into and out of ...
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3answers
934 views

Is a canonical transformation equivalent to a transformation that preserves volume and orientation?

We have seen the reverse statement: Lioville's Theorem states that canonical transformations preserve volume (and orientation as well). Is the reverse true? If I demand a map from the phase space to ...
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2answers
27 views

How can I conduct an experiment on the buring power of a 2 inch cubic block of wood?

I'm trying to help my son put together a science project and the hypothesis that we've come up with is this: If you take cubes of wood of the same volume (say 2 inches cubed) and start them burning ...
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1answer
444 views

Why does expansion in a vacuum cause gas particles to not do any work?

My lecture notes state that if gas particles sit in an insulating container, with a partition separating the gas from vacuum is removed, no change in internal energy is done, and it is stated that it ...
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1answer
191 views

Deriving $Tds$ relations in thermodynamics

The Tds relations I refer to are, $$Tds = du + Pdv$$$$Tds = dh - vdP$$ The first equation is derived (assuming internally reversible process) from the definition of entropy $ds = \delta Q/T$ and the ...
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1answer
34 views

Converting volume to dimensions

Not sure if this is better posted in mathematics, but I'd like to know the formula used to convert cubic meters to dimensions (eg: 1m height x 1m width x 1m length). I understand that you can turn ...
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2answers
81 views

Why is $\mathrm{d} \Omega = \mathrm{d} \cos \theta \mathrm{d} \phi$ and not $\mathrm{d} \Omega = -\mathrm{d} \cos \theta \mathrm{d} \phi$?

The textbook I am following (Peskin&Schroeder) on QFT takes $\mathrm{d} \Omega = \mathrm{d} \cos \theta \mathrm{d} \phi$. I cannot for the life of me see that its correct. We know that $\mathrm{d}...
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1answer
149 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
15k views

Hole in a water bottle

I understand that when you make a hole on a bottle filled with water and put the cap on tight the water will not flow out due to the atmospheric pressure acting on the hole. My confusion is that, lets ...
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6answers
331 views

How to measure the volume of a fish pond? [closed]

Suppose that the shape of a fish pond is irregular, so we can't use any simple math formula, e.g. width $\times$ length $\times$ depth, to find its volume. I'm wondering if, there's a good way of ...
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2answers
71 views

Question about work done in $P$-$V$ diagram [closed]

$$A_1 = 0.5 (0.2) (1.5 \times 10^5) = 0.15 \times 10^ 5 \text{Pa m}^3$$ $$A_2 = 0.2 (1.0 \times 10^5) = 0.2 \times 10^5 \text{Pa m}^3$$ $$\frac{A_\text{total}}{\text{Work}} = 0.35 \times 10^5 ~\text{...
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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
571 views

Pressure-Volume Diagram

Why does pressure start off high in the Pressure-Volume Diagram starting from a compressed liquid to a super heated vapor? Noting that the temperature is constant in the process,I can't seem to ...
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2answers
71 views

Why are $dT^2$ and $dT^3$ negligibly small?

With $dT^2$ I mean the square of the change in temperature. While deriving the relationship between the coefficient of linear expansion and of volumetric expansion, terms with $dT^2$ and $dT^3$ are ...
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1answer
120 views

Air breathing apparatus with pressure gauge and cylinder

I have got self contained air breathing apparatus with pressure gauge and cylinder. Cylinder has marking that it's 6 ltrs. When I open valve pressure gauge shows me 250 bars. Can I calculate the ...
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2answers
2k views

How to calculate the efficiency from a $p$-$v$ diagram?

Question: Calculate the efficiency of the real and ideal cycles. The process 1-2 is polytropic, 2-3 is isochoric, 3-4 is polytropic as well, and 4-1 completes the cycle with another isochoric process....
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1answer
414 views

Electric field of uniformly charged tetrahedron

How to calculate electric field of arbitrary tetrahedron with uniform charge density at arbitrary point? I got: 4 tetrahedron vertices total charge in Coulombs point at which I want to compute E ...
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1answer
297 views

Can you add helium to an already inflated soccer ball to make it lighter?

I was in a meeting today and a scenario was presented that began with two soccer balls of identical weight (both inflated). One of the balls then had helium added to it, and became heavier in the ...
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1answer
145 views

What does it mean for a particle to have volume? [duplicate]

As far as I understand, we do not know whether an electron is a point particle or not, but we have a very low upper bound for its potential volume. If it turns out that electrons do have volume, what ...
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1answer
54 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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1answer
604 views

How do scientists measure vapor pressure?

Experiment: We have a cylinder with a piston that is essentially weightless, frictionless, and exposed to atmospheric pressure. The cylinder has a volume of 2V, but half of it is filled with water and ...
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2answers
69 views

Is there a global minimum on theoretical information storage?

By "theoretical information storage" I mean future forms of information storage that can be stored, for example, atomically. I assume that atomic-level information storage is as small as information ...
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2answers
3k views

Why are temperature and specific volume independent properties?

The state postulate says that the state of a simple compressible system is completely specified by two independent, intensive properties. Two properties are independent if one property can be varied ...
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1answer
623 views

Stresses and strain : change of volume

I was reading about stresses and strains and I came across the concept of volumetric strain and am now having a slight conceptual difficulty. I used to believe that despite changes in linear and ...
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2answers
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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1answer
167 views

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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2answers
200 views

Can a drop of liquid splash as high as its origin?

Through the conservation of energy, a rubber ball will never bounce as high as there from which it is dropped. But are liquids subject to the same force? In particular, if I a pour liquid on the ...
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3answers
90 views

Volume Displacement Submergence Question (Read for details)

If a person's entire body is submerged in water, and they get an erection, will the water level ultimately be higher than before or not change at all?
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2answers
4k views

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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0answers
94 views

Keep steel cube afloat [closed]

I have 1000 kg cube of steel. How much of air(volume) needed to keep it afloat(on water)? I`ve been trying to find online calculator for this task, but with no success.
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0answers
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 ...