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Questions tagged [volume]

The tag has no usage guidance.

-2
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1answer
69 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 ...
2
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0answers
26 views

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 $\epsilon$....
2
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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 ...
1
vote
1answer
27 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 ...
1
vote
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 ...
0
votes
1answer
348 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 ...
0
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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 ...
1
vote
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 ...
0
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2answers
44 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 ...
0
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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)...
0
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1answer
164 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?
0
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2answers
32 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 ...
1
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2answers
39 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 ...
3
votes
3answers
214 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-...
5
votes
2answers
157 views

Volume Minimization Principle?

I know of two major extremum principles: Entropy Maximization: for a specified $(U,V)$, the equilibrium state has a higher $S$ than all non-equilibrium states, i.e., equilibrium occurs at the maximum ...
1
vote
1answer
35 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 ...
3
votes
2answers
163 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,...
1
vote
1answer
46 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 ...
11
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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?
0
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1answer
51 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?
1
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2answers
29k 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?
2
votes
3answers
1k views

Are $d^3r$, $d^3\vec{r}$, and $d^3{\bf r}$ the same as $dV$, the volume element?

I've seen the term $d^3r$, $d^3\vec{r}$, and $d^3{\bf r}$ being used instead of $dV$. Are they exactly the same? Do they have a different connotation?
0
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0answers
25 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 ...
1
vote
2answers
51 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 ...
0
votes
1answer
28 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 ...
9
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5answers
66k views

What happens to the temperature when an ideal gas is compressed?

I am rather confused about this. I know from Charles' law that under constant pressure, the volume of a gas is directly proportional to its absolute temperature i.e. $$\frac{V_1}{T_1} = \frac{V_2}{...
2
votes
1answer
90 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 ...
0
votes
1answer
76 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 ...
0
votes
1answer
148 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 ...
0
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0answers
61 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_\...
0
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2answers
43 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 ...
0
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1answer
28 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 ...
0
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1answer
34 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 ...
0
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1answer
62 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 ...
0
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2answers
35 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 ...
0
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2answers
153 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
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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 ...
0
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0answers
29 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 ...
1
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3answers
129 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 ...
-4
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4answers
634 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.
3
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1answer
423 views

Converting Sums to Phase Space Integrals in Statistical Physics

I'm familiar with the approximation of a sum over energy states by an integral over phase space: $$ \sum_n f(\epsilon_n) \approx \frac{1}{h^3}\int f\left(H(\textbf{r},\textbf{p})\right) \, d^3\textbf{...
2
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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 $...
3
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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 ...
0
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0answers
34 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, ...
0
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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 ...
0
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2answers
851 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 ...
0
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2answers
76 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, ...
0
votes
1answer
310 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 ...
0
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1answer
53 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 ...
4
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4answers
21k views

Why is it faster (as in proportion to volume) to boil 4 cups of water than to boil 2 cups?

I did an experiment where I boiled two cups (500ml) of water in a kettle, and it took 1:30 minutes to reach around 98 C, average. However, when I boiled 4 cups of water, (1L) it only took me 2:30 ...