What is Volume: Definition and 1000 Discussions

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or 3D shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.
Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. Volumes of complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.
The volume of a solid (whether regularly or irregularly shaped) can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of just one of the substances. However, sometimes one substance dissolves in the other and in such cases the combined volume is not additive.In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian invariant.
In thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure.

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1. Automotive Loss of gaseous volume because of fuel combustion

Hi, 1st and general case: 2 H2 and 1 O2 take up 1 liter of volume at, for example, 20°C, before combustion. After combustion and cooling down to 20°C, how much volume do the exhaust gases take up? Since the stoichiometric relationsship is 2 mols of H2 for every mole of O2, so those three moles...
2. Chemistry Question about Gas Law Problem

PV=nRT P*1L = 6 moles * 0.0821*298 (I added up all the moles and solved for pressure) P =146.79 atm 146.79 atm * V = 2 moles Ar * 0.0821* 298 (I plugged in the moles for argon and solved for volume) V= 0.333 L Answer key says the answer is 1 Liter. Where did I go wrong?
3. Please tell me the difference in the size of the air volume

Hi. Since I've been studying fluid mechanics, I've been asking a lot of questions Thank you all for your help! I suddenly have a problem that I want to think about while studying today. I would like to know the change of air volume according to the pipe shape as shown in the picture below...
4. I have a question about the air volume

Hello I need your help studying hydrodynamics. I have a question about the volume of air. Assuming incompressibility, non-viscosity, there is a coefficient of tube friction, and it moves in laminar flow... The Oulet stage Fan is installed, so air moves from top to bottom. The cross-sectional...
5. B Having trouble deriving the volume of an elliptical ring toroid

Like the title and the summary suggest, I can derive the volume ##V=2\,\pi^{2}\,r^{2}\,R## for a ring torus - a doughnut-style toroid (one such that the major radius ##R## > the minor radius ##r##, and it therefore has a hole at the center) that is of circular cross-section. But I want to be...
6. B Question about volume of a sphere

Hello everyone, I was trying to find volume of a sphere by doing some calculus, the area of a circle is ##{\pi}r^2## So I thought I would calculate the volume of one hemisphere and then multiply by two, but I got a different result than the standard formula, the standard formula is ##\frac 4 3...
7. I How large is the volume of a photon interacting with matter?

When a photon interacts with matter and diffracts, the photon seems to interact with the area of its wave front, determined by an aperture even if it is only one photon. But how far does it interact in depth? Does it always "feel" the whole crystal? Can we assume the photon is reflected by the...
8. How can I calculate the Density and Volume of a mechanical mixture (atoms)?

Is it correct that: density = [ 0.09 * (density of NaCl) ] + [0.91 * (density of water) ] volume = [ (volume of water) + ( { (volume of NaCl) / 48} * 9) ] Thank you so much for any advice.
9. Engineering Composition of flue gases by volume on a wet basis and dry basis

Butane 0.75mol of C4H10 0.75 x C4 = 3mol of CO2 0.75 x H5 = 3.75mol of H2O 0.75 x 6.5O2 = 4.875mol of O2 Propane 0.10mol of C3H8 0.10 x C3 = 0.3mol of CO2 0.10 x H4 = 0.4mol of H2O 0.10 x 5O2 = 0.5mol of O2 Butene 0.15mol of C4H8 0.15 x C4 = 0.6mol of CO2 0.15 x H4 = 0.6mol of H2O 0.15 x...
10. Volume's effect on buoyancy: Does pressure increase?

Hey! Im currently writing a lab on how an increase in the volume of an object will result in an increase of buoyancy force acting on an object. We fully immerse different amounts of clay playing blocks into water (using a string) on top of a scale, and calculate the buoyancy force. The reasoning...

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26. I Confusion about the interpretation of specific volume

So I'm reading through Cengel's thermodynamics textbook, and came across this solved example: Firstly, pressure in this context I'm assuming is vapour pressure? Since we're dealing with pure substances in this chapter. But what's confusing me is, here's the diagram I have: They've not...
27. B Need some clarification to get dimensions for a volume

I have a volume of 0.04 cubic centimeters. I need to convert into something I can work with in my shop. Tolerance is not important. To get dimensions of a cube with this volume, I calculated the cube-root which came out to 0.341. So, my cube would be (rounded) 3mm on a side, correct? Next...
28. (has been resolved)：Integral to find elbow volume

has been resolved Please help me to understand which answer is correct. I use the integral method to find the elbow volume as follows： But my book say：

34. Finding the Volume of a Slightly non-Rectangular Box

I have a storage tote that has a larger top than bottom. How do I figure out its volume? Is this like a 3D trapezoid? Can I measure the volume of the rectangle assuming the top is the same as the bottom, then as if the bottom were the same as the top, then just subtract the two?
35. Gas law problem (changing volume, temperature and pressure)

I can’t quite work my head around this question, I am having a difficult time analyzing the question, I can’t seem to make out what the initial and final conditions are would appreciate all the help I could get cheers
36. I Appearance of Warp Bubble Internal Volume to Distant Observer

At a single moment of coordinate time ##t##, would a distant observer perceive a warp bubble's interior volume as blown up, or would it seem compressed? Looking in the catalogue of spacetimes at the static local tetrad of the Alcubierre metric, the ##e^x_{(x)}## leads me to think that a static...
37. A Proper Volume on Constant Hypersurface in Alcubierre Metric

I'm wondering if there is a way to find the proper volume of the warped region of the Alcubierre spacetime for a constant ##t## hypersurface. I can do a coordinate transformation ##t=τ+G(x)##, where ##G(x)=\int \frac{-vf}{1-v^2f^2}dx##. This eliminates the diagonal and makes it so that the...
38. Estimating the Volume of a Cylindrical Shell

Using the equation above, I plugged in 5.5 inches for the radiu and 0.5 inches for the value of dr and then solved for the estimate of the change in volume, dV. However, the solution instead uses a value of 6 inches for the radius receiving a different estimate for the problem than I did. Is my...
39. I Which units is this conversion factor for (molar volume)? 0.023901488

I'm getting the wrong results when using an old, undocumented code and just realized there's a number lurking in it that I can't account for. It's: 0.023901488 and it is multiplied with molar volume and pressure. I have searched for a couple of hours but just can't figure out what the units...
40. Spirit evaporating from a bowl

Problem statement : I draw the problem statement above. I hope I am correct in inferring that the bowl is hemispherical. Attempt : I could not attempt to the solve the problem. We are given that the rate of change (decrease) in volume is proportional to the surface area ...
41. I Do volume integrals involve bounding surfaces?

In Vanderlinde page 171-172, the author derives the vector potential for the magnetic dipole (and free currents) \begin{align} \vec{A}(\vec{r}) &=\frac{\mu_{0}}{4 \pi} \int_{\tau} \frac{\vec{J}\left(\vec{r}^{\prime}\right) d^{3}...

46. Finding the volume of the solid

My attempt : ## \displaystyle\int_0^2 \displaystyle\int_0^{2-x} (2-2x -2y) dy dx = -\frac43 ## But it is wrong.
47. I Average electrostatic field over a spherical volume

this formula in the picture is the average electrostatic field over a spherical volume of radius R. It is the same expression of the electrostatic field, at the (position) of the point charge, of a volume of charge of uniform density whole entire charge is equal to (negative)q. My question is...
48. New volume of balloon after adiabatic expansion

Result My attempt
49. What has a shape but no volume?

I was reading a Chemistry book when I read about the three states of matter. Everyone knows what they are, but I didn't know the simplest way to describe each of the three until I read this book. It said that a solid has a shape and a volume, a liquid has no shape but has a volume, and a gas has...
50. I Computing Volume in General Relativity: Use of Tensor & Friedmann Eqns

When we compute the stress energy momentum tensor ## T_{\mu\nu} ##, it has units of energy density. If, therefore, we know the total energy ##E## of the system described by ## T_{\mu\nu} ##, can we compute the volume of the system from ## V = E/T_{00}##? If it holds, I would assume this would...