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40 votes

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

The question is a little hard to define because, as pointed out in the comments, it's not clear what the "outside volume" is, or how to define it in curved space to compare it to regular space. Still, ...
Javier's user avatar
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29 votes
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Does curved spacetime change the volume of the space?

In a question like this you need to ask what does the volume change relative to. So it's a little bit ambiguous. However, the answer to your question is "yes" in the following restricted sense. ...
Selene Routley's user avatar
26 votes

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

Surprisingly, the answer is yes. Or at least, yes, if you rephrase the question a little bit. As you might know, gravity can deform spacetime. (actually this is not completely true, it is actually ...
Crimson's user avatar
  • 2,871
19 votes

Why is the ratio of two extensive quantities always intensive?

It is mainly a mathematical reason. Extensive quantities grow with system size. If two quantities scale in the same way with a variable (in this case system size), it cancels out in the division. ...
lmr's user avatar
  • 1,304
17 votes
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Is a canonical transformation equivalent to a transformation that preserves volume and orientation?

In dimension $2n>2$ they are not equivalent since (for time-independent transformations) canonical is equivalent to $$\sum_{k=1}^n dq^k\wedge dp_k = \sum_{k=1}^n dQ^k\wedge dP_k\tag{1}$$ whereas ...
Valter Moretti's user avatar
16 votes

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

The physical concept most closely mimicking the experience of fantasy items like bag of holding is a traversable wormhole. Essentially, it is a connection between two different regions of space, a ...
A.V.S.'s user avatar
  • 15.6k
15 votes

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

I'd like to add another option to the answers provided by Javier and Crimson. There is a spacetime geometry popularised by Wheeler (I'm not sure it originated with him) called the bag of gold ...
John Rennie's user avatar
14 votes
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Tip of the Iceberg

The upward buoyancy force on the iceberg is equal to $$F_{b}=g\rho_{{\rm water}}V_{{\rm under}},$$ in terms of the acceleration of gravity, the density of the liquid phase of water and the volume of ...
Buzz's user avatar
  • 16k
13 votes

Am I making a fatal error with this simplification?

That's not right, unfortunately. The principle governing this situation is the continuity equation, which says that the total flow rate past any given point is constant. Since the flow rate is given ...
J. Murray's user avatar
  • 68.7k
12 votes

Why do quantum objects slow down when volume increases?

This is a loosely-phrased consequence of the uncertainty principle, which says that the product of the position uncertainty and the momentum uncertainty is larger than some minimum value that you can ...
rob's user avatar
  • 88.6k
11 votes

Can we change the volume of a wire by applying force on it in order to stretch it, if yes is there any way to calculate it?

The volume will change while tension force is still being applied. You can calculate the change using Poisson's ratio for the material. But when you release the tension the wire will return to its ...
alephzero's user avatar
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10 votes
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Is it a coincidence that 1 liter water has a mass of 1 kg while 1 cubic meter has 1000 liters of water?

It is not a coincidence. As the Wikipedia article on the Litre says: One litre of water has a mass of almost exactly one kilogram when measured at its maximal density, which occurs at about 4 °C. ...
ACuriousMind's user avatar
  • 124k
10 votes

The actual proof of $\delta W = P dV$

$$\delta W=F\delta x=F\frac{\delta V}A=\frac FA\delta V=P\delta V$$
Steeven's user avatar
  • 50.5k
9 votes

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

Counterexample: The transformation $$Q^1~=~2q^1 ,\qquad P_1~=~p_1,\qquad Q^2~=~\frac{1}{2}q^2 ,\qquad P_2~=~p_2 $$ preserves phase space volume & orientation, but is not a symplectomorphism.$^1$ ...
Qmechanic's user avatar
  • 200k
9 votes

Am I making a fatal error with this simplification?

The tip cannot come to a point - otherwise the water cannot escape from its end - so actually its shape is a truncated cone also known as a conical frustrum. You say If water is flowing through the ...
gandalf61's user avatar
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8 votes
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How do pressured containers within pressured containers behave?

As you suggest, you could use a large number of nested containers to gradually increase the pressure of the innermost container to very large values. Generally it's only the pressure difference that ...
tom10's user avatar
  • 2,847
7 votes

Volume of a Photon?

In the quantum regime the answer to such questions really depends on what you mean by "volume". A photon has no volume in the sense that it can theoretically be confined in an arbitrarily small ...
glS's user avatar
  • 14.2k
7 votes

How to measure the volume of a fish pond?

For a fairly exact measurement, I would take some harmless chemical that's easy to detect, and pour a certain volume in and let it dissolve/diffuse completely. Then, measure it in ppm, do the ...
Señor O's user avatar
  • 7,460
7 votes
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Why is there a volumetric dimension to pressure-volume work?

Note that the volume is not the system volume but the displaced volume, or the volume exchanged by moving an interface against a pressure resistance. With this in mind, yes, if the resistance is a ...
Chemomechanics's user avatar
7 votes

Why is entropy an extensive property?

There is some ambiguity in how entropy is defined in thermodynamics/stat. physics, as, e.g., discussed in this answer. To take the two most common definitions: In thermodynamics entropy is defined ...
Roger V.'s user avatar
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7 votes
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The actual proof of $\delta W = P dV$

For a general material volume $V$, you can write the power of surface force acting on its contour $\partial V$ can be written as $\dot{W} = \displaystyle \oint_{\partial V} \mathbf{t}_n \cdot \mathbf{...
basics's user avatar
  • 8,176
6 votes

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

Consider two devices: A gas law demonstration apparatus measures temperature and pressure during compression. This device slowly lowers a piston in a thin walled container, resulting in mostly ...
brielmannh's user avatar
6 votes
Accepted

Is it possible for two gases to have different internal energy but equal pressure and temperature?

The equation of state does not tell everything about a thermodynamic system. Moreover, the specific heat is not related to the value of the internal energy but to the variation of internal energy when ...
GiorgioP-DoomsdayClockIsAt-90's user avatar
6 votes
Accepted

Intuition about conservation of volume in phase space (Liouville's theorem)

Not a demonstration, but maybe something more visual than the other correct answers. Instead of being in 2D like you suggest, let's try to see what happens in 1D when the particles move "radially&...
Syrocco's user avatar
  • 953
6 votes
Accepted

What is the "volume of the gauge group"?

Weinberg apparently means that the global Lie group $G$ is a finite-dimensional Lie group, typically $G=SU(N)$, while the gauge group ${\cal G}$ is the set of maps from spacetime $M$ to $G$. If $M$ is ...
Qmechanic's user avatar
  • 200k
5 votes
Accepted

How to derive that $\delta w = - PdV$?

It seems to me that you've gone round in a circle. What's wrong with this simple argument? Suppose that the fluid exerts a force $F_n$ on a small area $A$ of the container wall, in a direction normal ...
Philip Wood's user avatar
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5 votes
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Approximation for the square of a Dirac delta function

The box normalization isn't motivation for setting $e^{ix(p+q-k)}=1$; Zee is just comforting those readers who (correctly) balk at the idea of squaring a delta function by reminding them that all of ...
J. Murray's user avatar
  • 68.7k
5 votes
Accepted

How can $1/V$ be equal to $0$ in Boyle's Law?

Formally we have $$ \lim_{V\rightarrow \infty} \frac{1}{V}=0 $$ I.e. the statement is true in the limit of infinite volume. For an ideal gas, this can be interpreted as saying that as the confining ...
gabe's user avatar
  • 1,212

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