Questions tagged [volume]
The volume tag has no summary.
543 questions
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Differential definition of mass density vs integral definition in continuum mechanics
In continuum mechanics, one often assumes that physical quantities are continuous in time and space. As such, one models for example density, $\rho = \rho(\mathbf{r},t)$, as a function which is ...
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Does it take longer to melt one big piece of ice or many small pieces of ice?
EDIT: Wow! Thank you so much everyone for your kind responses! I truly appreciate it! Just a note, the medicine I take needs to be stored between 2°C to 8°C.
Reposting from Math.SE as recommended (...
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Will one big ball of ice melt at the same rate as many small balls of ice (assuming they both have the same volume)? [duplicate]
This question is based of a real problem I am facing. Over the winter holidays, I need to travel to a different country. I need to transport medicine, and the medicine has to remain below a certain ...
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Riemann 2-manifold volume form: complex vs real
Question 1: is it always possible to write the metric in that form? Is it sufficient the local conformally-flat form to obtain the volume?
Question 2: Is the volume form in (4.1) well-defined? Going ...
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Alternate statement for Liouville's theorem: Can you say that the relative velocity between any two representative points is zero?
So Liouville's theorem basically says the local density of representative points stays constant or that the flow of representative points resembles that of an incompressible fluid. Can you then say ...
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How can we define the radius of a black hole?
I just came up with an intuitive way. While we can’t actually put a meter stick inside the event horizon to measure the radius, we can draw a concentric circle slightly bigger than the event horizon ...
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Why does a free-falling liquid jet contract while an upward jet expands, from a molecular perspective?
I’m trying to understand this strictly from the atomic/molecular level, without relying on equations of continuity. Consider this situation:
A vertical water jet is released in free fall (downward).
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Clarification about Kittel and Kroemer's remark about constant photon entropy processes
For Planck's radiation law, Kittel and Kroemer write in Thermal Physics,
The entropy of the thermal photons can be found from the relation
(3.34a) at constant volume: $d\sigma = \frac{dU}{\tau}$, $
\...
- 1,149
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How to do physics on non-orientable surfaces?
Non-orientable surfaces don't have a volume form on it. How do you define the action principle without a volume form? I know somehow string theory is routinely done on non-orientable surfaces but I ...
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What limits the shape of the $pV$ diagram for an engine? [closed]
Here is my best understanding of a 4-stroke engine $pV$ diagram:
The net work done is (area of the main loop) - (area of the pumping loop).
If you want to calculate the efficiency (assuming ideal gas) ...
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In a simple, single-phase, single-component, compressible system, are $(p,V)$ sufficient to give a complete description of the system state?
I know that the state postulate applied to a simple, compressible, single-phase, single-component system means that any two independent intensive variables are sufficient to determine the state of a ...
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Increasing the volume of a perfect vacuum
This question is theoretical - I'm not concerned with real-world, practical limitations.
Imaging a container, say 1 litre in volume in which is a perfect vacuum.
What happens inside the container if ...
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A pattern about partial derivatives of two extensive variables while keeping intensive variables constant
My lecturer proposed the following, which is
$$
\frac{∂\text{Extensive}}{\text{∂Extensive}}\bigg|_{\text{Intensive}} = \frac{\text{Extensive}}{\text{Extensive}}
$$
where 'extensive' represents an ...
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Curvature of spacetime from differences in spatial volume?
Is it possible to view spacetime curvature ($g_{mn}$) just as differences in a spatial volume |g_ij|, (i,j = 1...3) while time goes differently fast at different places (inverse of spatial volume: ...
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Doubt regarding center of mass of a cone
I would just like to confirm that if I have a solid cone of uniform density and I make a plane cut such that the 2 parts obtained have an equal mass, is it correct to state that the center of mass of ...
