Questions tagged [volume]

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10
votes
3answers
94k views

Thermodynamics - Sign convention

I use the sign convention: Heat absorbed by the system = $q+$ (positive) Heat evolved by the system = $q-$ (negative) Work done on the system = $w +$ (positive) Work done by the system = $w -$ (...
28
votes
5answers
4k views

Does curved spacetime change the volume of the space?

Mass (which can here be considered equivalent to energy) curves spacetime, so a body with mass makes the spacetime around it curved. But we live in 3 spatial dimensions, so this curving could only be ...
7
votes
2answers
4k views

Do black holes have infinite areas and volumes?

How to calculate the area / volume of a black hole? Is there a corresponding mathematical function such as rotating $1/x$ around the $x$-axis or likewise to find the volume?
1
vote
1answer
337 views

Thermodynamics - internal energy

What would the curve that describes the change of internal energy ($U$) with the volume ($V$) be like if the change in the temperature is negative? My try: For a ideal monoatomic gas, we have $U=(3/...
1
vote
4answers
18k views

Specific heat capacity at constant volume VS constant pressure

For an ideal gas, why is the specific heat capacity at constant volume lower than the specific heat capacity at constant pressure?
10
votes
5answers
69k 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}{...
3
votes
4answers
38k views

What kinds of materials contract the most in cold temperatures?

I know that water expands in the freezer, but I'm curious about which materials contract in response to cold temperatures --- and most importantly, which ones undergo the most drastic changes?
1
vote
3answers
4k views

Does the volume of a thermodynamic system always have to change for it to do work?

Does the volume of a thermodynamic system always have to change for it to do work? If yes,could you explain why? And if no, could you provide the example of a system, where it is not neccesary.
2
votes
2answers
995 views

How does cooling scale with volume?

What equation would give me the answer to the question, "If i have a cup of water at a tempature of say boiling, how long would that cup of water take to cool off compared to say half that size of a ...
2
votes
2answers
11k views

How does the bulk modulus of air change with rising pressure?

I can't seem to find the answer to what should be a trivial question: I have a rigid air-tight container of fixed volume and I am pumping air inside. The pressure is increasing (very slowly) from ~...
0
votes
1answer
469 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 ...
-2
votes
5answers
147 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{\...
8
votes
2answers
2k views

Do you pay more for gas when the day is warmer?

Found this at the gas station yesteday - got me thinking...
3
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2answers
5k views

Excluded Volume Calculation in Van der Waals Equation

When accounting for the excluded volume for in the Van der Waals equation, it is assumed that the molecules are hard spheres and are of diameter. If we consider a cube of volume V, then we can say ...
3
votes
2answers
3k 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....
2
votes
1answer
722 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 $$A=4\pi r^2=\frac {16 \pi G^2M^2} {c^4}$$ ...
1
vote
1answer
386 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 ...
1
vote
1answer
912 views

What does Liouville's Theorem actually mean?

Basically, the mathematical statement of Liouville's theorem is: $$\frac{\partial \rho }{\partial t}= -\sum_{i}\left(\frac{\partial \rho}{\partial q_i}\,\dot{q_i}+\frac{\partial\rho}{\partial p_i}\,\...
1
vote
4answers
6k views

Why is density an intensive property?

I am still trying to understand what are intensive and extensive properties. Possibly someone can give a pointer to a decent text (preferably on the web), as I am not too happy (to say the least) with ...
0
votes
2answers
1k views

Point masses and infinite densities

Point masses are masses who don't have volume. It is said that they are infinitly dense, but I though division by zero is undefined hence you can't define the density for a point mass because $\rho=m/...