Questions tagged [volume]
The volume tag has no summary.
53 questions
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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 = $w -$ (...
- 275
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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 ...
- 421
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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?
- 1,073
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Liouville's theorem and conservation of phase space volume
It can be proved that the size of an initial volume element in phase space remain constant in time even for time-dependent Hamiltonians. So I was wondering whether it is still true even when the ...
- 28k
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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/...
- 133
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4
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Why is entropy an extensive property?
Question. Why is entropy an extensive property? How can we prove that for the general case?
Is that why $S(k N)=kS(N)$? I am interested in answer based on classical thermodynamics.
Actuality. ...
- 321
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5
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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.
$$\frac{V_1}{T_1} = \frac{V_2}{...
user36790
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What does Liouville's Theorem actually mean?
Basically, the mathematical statement of Liouville's theorem is:
$$\frac{\partial \rho }{\partial t}= -\sum_{i}\left(\frac{\partial \rho}{\partial q_i}\,\dot{q_i}+\frac{\partial\rho}{\partial p_i}\,\...
user36790
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Determine the Dependence of $S$ (Entropy) on $V$ and $T$
Why can the equation $$dS= \frac{1}{T} dU + \frac{P}{T} dV$$ be expressed as $$dS= \left. \frac{\partial S}{\partial T} \right|_V dT + \left. \frac{\partial S}{\partial V} \right|_T dV \quad?$$
- 87
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Minimal phase space volume $h^3$ out of Heisenberg's principle
So the explanation in my text book is this: we have a phase space volume $\Delta x\Delta y\Delta z\Delta p_x\Delta p_y\Delta p_z$. Now they state that Heisenberg's uncertainty principle states $\Delta ...
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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.
- 135
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4
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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?
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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 ...
- 133
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What does it mean for the Lorentz Transform to preserve areas?
If we look at the Lorentz Transform from some frame $S$ to some frame $S'$ moving relative to $S$...
$$\begin{bmatrix}
\gamma & -\gamma v\\
-\frac{\gamma v}{c^2}& \gamma
\end{bmatrix}\begin{...
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How does Pressure times Volume = Work Done?
I understand the equation mathematically-- $p$ times (change in) $V$ = Work done. However, I am confused about it conceptually. Work is (in a non-calculus context) constant force applied over a set ...
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