Questions tagged [volume]

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68 views

Question about using Liouville's theorem to calculate time evolution of ensemble average

With the Liouville's theorem $$\frac{{d\rho }}{{dt}} = \frac{{\partial \rho }}{{\partial t}} + \sum\limits_{a = 1}^{3N} {(\frac{{\partial \rho }}{{\partial {p_a}}}\frac{{d{p_a}}}{{dt}} + \frac{{\...
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25 views

Relationship between pressure, chamber volume, and flow rate? [closed]

It has been a while since I took any classes involving fluid mechanics, so bear with my phrasing. I am trying to pump water using a peristaltic pump (Masterflex C/L) with tubing that has about a 1 mm ...
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0answers
23 views

Calculating infinitesimally small volume of a sphere in velocity space

This link (at the end of the page) is deriving the formula to calculate an infinitesimally small volume $dV$ on the surface of a sphere with radius $v$ in velocity space. It states that $dV = ...
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3answers
120 views

Shape of isotherms in $P$-$V$ phase diagram

Please explain the shape of the isotherms in this P-V phase diagram. In particular, why are the isotherms flat in the liquid-vapor region? (image from Lumen Learning | Physics | Phase Changes)
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3answers
65 views

$pV$ work and Specific volume [closed]

I am working on a $pV$ work exercise. I am given $P_1$, $P_2$, and $V_1$; we can solve for $V_2$. I am also given mass. I am told that the $pV$ relationship is $pv^{1.2}=const.$, where $v$ is ...
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3answers
75 views

Energy Density is expressed in Liters, Liters of What?

When looking at energy density of batteries it is often expressed as Wh/L. For instance, Wikipedia says Lithium Ion batteries have a density of 250–693 W·h/L. Liters is supposed to express the volume ...
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2answers
68 views

What is the volume occupied?

What is the volume occupied by 1 mole of gas at $10^{−10}$ torr, the pressure inside an “ultra high vacuum” (UHV) chamber. How do I solve this problem without being given the temperature?
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1answer
100 views

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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1answer
29 views

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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0answers
44 views

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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3answers
73 views

Sign of $(\partial T /\partial V )_E$

Consider a realistic gas. If it is insulated and then allowed to expand into a vacuum, how does its temperature change? We have to consider the sign of $\left(\dfrac{\partial T}{\partial V }\right)...
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2answers
46 views

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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2answers
39 views

What is the volume of liquid propane consumed when measuring gas flow at a given pressure?

We have a building with a large propane cylinder that distributes propane to different sources within the building. When the cylinder is filled, the propane is compressed to a liquid, and our bill is ...
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2answers
42 views

Change in Volume of Objects on applying stress

I came across a statement that whenever any stretching or compressing is done on any object, its change in volume is always greater than $0$. This means that density always decreases (mass remaining ...
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3answers
221 views

Why is there Net Work Done on a Pressure/Volume Cycle?

The area enclosed by the rectangle is said to be the Net Work Done. My question is why would there be any net workdone if it returns to its initial position (W). Shouldn't it act like a force-...
1
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1answer
39 views

Relationship between volume and surface density

I was not sure if it fits better here, or in the math forum, but this is the problem I am trying to solve: Say you have a full cylinder of radius $R$, height $L$, and its uniformly charged with ...
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2answers
189 views

What is the volume inside the event horizon of a black hole?

As I understand it, we measure things like distance (and volume) by the speed of light. A meter is the distance light travels in 1/299792458 seconds. In "normal space" this is (barely) straightforward,...
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1answer
48 views

Definitions of area and volume in $d$-dim spacetime

I am reading Erik Verlinde's paper "Emergent Gravity and the Dark Universe". Equations 2.12 and 2.13 give the area $A(r)$ and volume $V(r)$ respectively. Do $d$ dimensions comprise of both space and ...
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1answer
1k views

Why is the ratio of two extensive quantities always intensive?

Is this something that we observe that always happens or is there some fundamental reason for two extensive quantities to give an intensive when divided?
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0answers
26 views

How can I get the height that sits above the waterline of a partly-submerged object?

If I know the density of water (say 1024 kg/m^3) and the density of ice (say 900 kg/m^3), and the volume of an object (say 8 x 10^9 m^3), how can I figure out how much of it is sitting above or below ...
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2answers
63 views

What happens to pressure when a liquid turns into a gas in a confined chamber?

I'm doing an experiment requiring immense pressures. Since I do not have access to a pump that can create these pressures I settled on something different... Instead of using a pump I want to utilize ...
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1answer
29 views

Determining Gas Constant $R$ from Boyles Law?

I have done an experiment (Boyles Law experiment using Boyles Law Apparatus) in order to determine the value of the gas constant $R$. I have also taken into account the dead space volume in my ...
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1answer
93 views

Is 1 liter always equal to 1 cubic decimeter, independently of temperature, pressure, etc?

I recently found this conversion table for the unit conversion $\rm mmol/m^3 \ \leftrightarrow\ \rm mmol/L$ (millimoles per cubic meter to millimoles per liter) My physics is very rusty, but just to ...
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1answer
68 views

What process is it when the polytropic index $n$ is equal to $- \infty$?

From $$Pv^n = \mathrm{constant}$$ When $n = - \infty$ What kind of process is it.... Eg... When $n= \infty$, It is constant volume.... Therefore when $n =- \infty$... What is constant?
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1answer
85 views

How to calculate the mass of gas needed to fill a cylinder to a certain pressure?

I m tasked with a tricky situation. I need to calculate the exact amount a tank can take in gas. But I dont know the volume of the tank. I just need to make sure that the tank reaches the right ...
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0answers
63 views

Volume expansion rate

In the paper Backreaction in late-time cosmology by Thomas Buchert and Syksy Rasanen, Annual Review of Nuclear and Particle Science 62 (2012) 57-79, in eq .2.2 the covariant divergence: $$\nabla_\...
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2answers
52 views

Change of specific internal energy due to temperature and volume

The change of internal energy due to temperature and volume may be written as $$ dU=C_V dT + \left( T\left(\frac{\partial S}{\partial V}\right)_T-P\right) dV$$ where $$\left(\frac{\partial S}{\partial ...
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1answer
30 views

Two containers that have the same volume (let say 500 liter) but are different in shape

I remember from school, one time a teacher explain us the following: two containers of the same volume, but one is thin and tall, and the second is short and wide. then if we fill them with water from ...
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1answer
38 views

Is specific volume a function of temperature only (in liquids)?

As far as I know, you can take the equation $pv=RT$ (with $v$ being the specific volume) for ideal gases. But I had a question in a quiz asking about this, and the answer was "dependent on ...
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1answer
66 views

An issue with thermodynamic properties of infinite systems

I have the following problem. Given a finite system, let us say a box of side $L$ containing $N$ "ideal gas" non-interacting particles, properties such as the entropy can be defined, in this case, $S ...
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0answers
32 views

Is there an influence of the air humidity on the air expansion by a temperature change?

I have found the following formula to calculate the expansion of air by a temperature change, if the pressure stays at the same level: ΔV = ​ɣ * V0 * ΔT This would give me an expansion of 46.96m3 in ...
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2answers
37 views

$p$-$V$ diagram and internal energy

I recently learned that if the initial state is equal to the final state in the $p$-$V$ diagram then the internal energy is equal to zero so that means $Q=W$. My question is how can you know that only ...
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3answers
163 views

What's the difference in a PV diagram that is curved versus one that is straight?

So what would the difference be between the graph above versus one that has the same inital and final points but the path is curved. I'm sure it has something to do with temperature, so does it mean ...
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2answers
61 views

What is the point of generalizing a more specific result to an order of magnitude?

In my textbook, an example wants me to find an estimate of the number of cells in a human brain. It gives the volume of the brain as $8 \times 10^{-3}\ \rm m^3$ which it then estimates further as $...
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0answers
35 views

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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4answers
643 views

Is it possible to find the volume of a 4 dimensional object? [closed]

I know there is 4 dimensional objects due to communicating with my friend group. I never found how would you find the volume because it was off the science channel.
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0answers
27 views

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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2answers
91 views

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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1answer
384 views

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 ...
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1answer
59 views

PV diagram of pure substance

Why does the specific volume of saturated solid state of water decreases with increasing pressure and the specific volume of saturated liquid wrt vaporisation increases with pressure? Can anyone ...
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2answers
66 views

Does Avogadro's law only apply to ideal gases?

I know the ideal gas law may change a little when for real gases or diatomic ones does Avogadro's law change too or does it stay the same?
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2answers
55 views

Why are the volumes above and below the center of mass of a uniform cone not the same?

So today in my physics class we derived the center of mass of a uniform cone, and it all made sense, but near the end of class a student asked, "If you were to split an object into two parts with ...
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1answer
604 views

Black Hole Surface Area-Mass Equation

Lets suppose we have a BH with mass $M$ and surface area $A$. From the Schwarzschild raidus we can say that the Area of the BH is proportional to its mass $$A=4\pi r^2=\frac {16 \pi G^2M^2} {c^4}$$ ...
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1answer
64 views

Relationship between binding energy of atoms in a solid and compressibility defined by bulk modulus

Consider an atom which has η nearest neighbours. The equilibrium binding energy $L_0$ of $N$ atoms is: $$ L_0 = \frac{Nηϵ}{2} $$ The bulk modulus $K$ of a solid of volume $V$ compressed under pressure ...
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0answers
35 views

Distance Dependence of Van Der Waals Forces and his Equation of State

I've been trying to reconcile the form of the van der Waals equation of state and the equations from which they are derived. Stop me where I go wrong: The VDW EOS includes two terms: one for the ...
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1answer
54 views

How to know heat flows out or in from a $pV$ diagram? [closed]

How to know heat flows out or in from $pV$ diagram?
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5answers
145 views

Why does the energy of a thermodynamic system depend on the volume?

In thermodynamics one assumes that the energy (or other observables) of the system only depend on a few parameters like the temperature, the particle number and also the volume: $dE = \left(\frac{\...
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0answers
29 views

Spacing of atoms in a cubic meter [closed]

I want to figure out the spacing between neighbouring atoms in a cubic meter of a large amount of 10^17 atoms were placed in perfect cubic structures within the cubic meter. I’m not sure how to go ...
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0answers
18 views

Volume in first octant

Here we are finding number of state less than energy E for particle trapped in 3D harmonic potential .For large value of E as compare to hw , we assumed energy levels as continuous.And we introduces ...
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1answer
76 views

What is the real definition of density? [closed]

What does density really mean? Everyone just provides me with the equation of finding density whenever I ask this question.