Volume Definition and 1000 Threads

I have a project I am working on that requires me to calculate the overall volume of propane tanks and the volume at a set distance from the bottom of the tank. The tanks come in two major configurations, ellipsoid ends with elliptical tank or hemispherical ends with cylindrical tank. I think...

In several books I have seen the statement that due to Heisenbergs principle no particle can be localized into a region of phase space smaller than ##(2 \pi \hbar)^3##. However, Heisenbergs uncertainty principle states that ##dx dp \geq \hbar/2## -- so a direct translation of this should imply...

Recently I've been researching the pressurization of water through the releasing of the waters of hydration in hydrates. The goal is to create a volume difference inside a container of fixed volume, basically the volume of the contents should be greater than the volume of the container in order...

Homework Statement I'm given length, width and height of the box, all have uncertainties.Homework Equations V=lwhThe Attempt at a Solution I've tried V=lwh, wasn't correct. Then V=lwh x (1 + relative uncertainty), wasn't correct. I just have no idea what the "best" value of a box is, my lab...

Hello, I am having some difficulty with levenspiel plots, in particular when dealing with a CSTR and when the reaction rate is increasing with conversion. I will give an example plot to demonstrate my point. Assume we are trying to find the volume of a CSTR necessary to reach a conversion of...

A gas analysis on a gaseous mixture gives 60% methane and 40% ethylene by volume. You need to store 12.3 kg of the mixture in a cylinder of volume 0.0514 m^3 at a maximum temperature of 45°C. Determine the pressure (kPa) inside the cylinder by: a. assuming that the mixture obeys ideal gas law...

Homework Statement Two pounds of water vapor at 30 psia fill the 4ft^3 left chamber of a partitioned system. The right chamber has twice the volume of the left and is initially evacuated. Determine the pressure of the water after the partition has been removed and enough heat has been...

Homework Statement Let R be the region in the first quadrant bounded by all three of the curves x = 2, y = 1, and y = (x−4)^2. Compute the volumes V1, V2, and V3 of the solids of revolution obtained by revolving R about the x-axis, the y-axis, and the x = 5 line, respectively. FIRST, I...

Homework Statement Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y=2x+15 and the parabola y=x2 about the following lines: a) The line x=5 b) The line x= -3 c) The x-axis d) The line y=25 Note: leave answer in terms...

Homework Statement Hi I require to compute the volume of a ellipsoid that is bounded by two planes. The first horizontal (xy) plane is cutting directly along the mid-section of the ellipsoid. The second horizontal plane is at a z = h below the first horizontal plane. The volume of the...

Homework Statement Find the area given by y=x^2, y=4, x=0 and revolved about y = -2 Use either the washer or shell methodHomework Equations Shell; integral from a to b of 2∏x(f(x))dx The Attempt at a Solution Alright so I tried to do this is terms of dy so since we are revolving about y=-2...

Homework Statement It's not so much an exact question. One of the things I need to figure out to answer my question is if there is a formula of some sort that helps me calculate volume change through a phase change. The final volume of a liquid that vaporizes into a gas, if the temperature and...

In Kittel's solid state text, problem 2.3, he says that the volume of the Brillouin zone is the same as a primitive parallelepiped in Fourier space. Somehow I can't see why this is true. Can someone help me see why this is true? Also, is the same relationship true between Wigner-Seitz cells and...

This is from a physics course, but felt more appropriate to post here. I just want some sanity checking on my procedure, since I'm not this far in my calculus course yet but am having to work through it anyway for physics. I have no idea how to approach part c, not even an inkling of where...

Given sphereRadius and piVal, compute the volume of a sphere and assign to sphereVolume. Look up the equation online. Use (4.0 / 3.0) to perform floating-point division, instead of (4 / 3) which performs integer division. Sample program: #include <iostream> using namespace std; int main() {...

This actually isn't a homework problem -- I'm just trying to understand an example in my textbook. The example shows how to calculate the volume of a cylinder (maybe it's actually a shell, I'm not sure) using an integral, but it occurred to me that I should be able to simply "unwrap" the...

Must double integrate using type I or type II planar region D to find volume bounded by Cylinder y^2+z^2=4 And Planes X=2y X=0 Z=0

Homework Statement A 1.0 μA proton beam is accelerated across a potential difference of 1.0 kV. Assume the beam has uniform current density over a diameter of 2.0 mm, and zero outside. Find: volume charge density in the beam, (HINT use λ=I/v where λ= charge/ unit length) The radial...

Maybe I'm plugging my website but I just finished writing a versatile cylinder calculator. If you know two variables (Volume Area Radius Height), it calculates the other two. http://www.1728.org/diam.htm It was a little tricky deriving the formulas but I'm glad I did. (Yes, I know if you...

Dear everybody here, please i need help at that attached image of round shape as shown, my questions is what is the formula which used for calculating the volume of that shape?, the cylinder of D1, and D2, , easily can be calculated by (Pi/4*D2*L), so how about in the middle? will...

Homework Statement I ran into this tough integral. I am asked to compute the volume of the following region using a double integral with ##a, b, c > 0##. The first octant region bounded by the co-ordinate planes ##x=0##, ##y=0##, ##z=0## and the cylinders ##a^2y = b(a^2-x^2)## and ##a^2z =...

"Volume of a primitive cell is independent of the choice of the cell." Why?

A solid is generated when the region in the first quadrant enclosed by the graph of , $$y=(x^2+1)^2$$ The line $$x=1$$ , the x-axis, and the y-axis is revolved about the x-axis. Find the volumn $$ V=\int_{a}^{b}\pi\left[f(x)\right]^2 dx =\int_{0}^{1}\pi\left[\left(x^2+1\right)^2\right]^2 \,dx...

Hi, I understand that Volume of Distribution (Vd) = elimination constant (k) * Clearance (Cl), but I can't visualize why clearance would be proportional to volume of distribution. Can someone help explain this to me? I feel like it should be a more complicated relationship. Clearance = Mass...

Homework Statement In the equation dm = δ x 2∏rLdr Where δ = density, and 2∏rL = volume How is it that the volume can be 2∏rL? The units of r is (metres) and the units of L is (metres) which leads to m2 (Area) Should it not be ∏r2L for volume? The Attempt at a Solution...

find the parallelepiped determined by the vector $a= \left\langle 1,2,3 \right\rangle$, $b= \left\langle -1,1,2 \right\rangle$, $c= \left\langle 2,1,4 \right\rangle$ find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. $P(-2,1,0)$, $Q(2,3,2)$, $R(1,4,-1)$, $S(3,6,1)$ 1...

I have a sealed syringe with air at known pressure P1, temperature T1 and volume V1. at some time I increase the volume of the syringe to V2, what will be the temperature T2 and pressure P2 at volume V2, right after the system reach to volume V2? The volume change process is relatively fast...

Hi :) I'm doing my A-Levels and have a maths investigation project for which I decided to model the working of a shishi-odoshi. (http://en.wikipedia.org/wiki/Shishi-odoshi) The shape of the water in the shishi-odoshi is a cylindrical segment and I want to use integration to find the...

Homework Statement Maximise the volume of a rectangular prism with the following constraints: the surface area must equal 2m^2 and the total edge length must be 12m. Homework Equations Using Lagrange multipliers, we construct the function we want to optimise with h(x,y,z, λ_{1}...

I encountered a problem where the answer I got was negative. Calculate the volume bounded by $y=x^2-5x+6$, $y=0$, about y-axis. An easy question that is best done with the cylindrical shell method: $$V=2\pi \int_{2}^{3} x(x^2-5x+6)\,dx$$ $$V=\frac{-5\pi}{6}$$ I think I know why it's...

Folks, I am having difficulty correctly representing a mechanical system within a correct "control volume at an instant" in order to identify the various energy balance terms given below ##\displaystyle \dot E_{st}=\frac{d E_{st}}{dt}=\dot E_{in} - \dot E_{out}+ \dot E_g## (1) that...

Homework Statement Determine the mass of object A if it is placed in a test liquid that has a specific gravity of 2. The object was placed in the liquid and the recorded submerged volume of the object was found by measuring the displacement of water which is 150 cm^3. Homework Equations...

A simple example at: http://blog.sciencenet.cn/blog-629442-600007.html I will translate the talk later.

Region bounded by $$x^2-y^2=16, y=0, x=8$$, about y-axis Integrating with respect to y, my lower and upper bounds are $-4\sqrt{3}$ and $+4\sqrt{3}$, respectively. $$V=\pi \int_{-4\sqrt{3}}^{4\sqrt{3}} 64-(16+y^2)\,dy$$ $$=2\pi \int_{0}^{4\sqrt{3}} 48-y^2\,dy$$ $$=2\pi (192\sqrt{3})$$...

Folks, It's been a while since I've done calculations like this so I was wondering if someone can help me calculate the volume of a gas at a specific temperature as compared to its liquid volume when measured below its boiling point. I can't seem to find a phase diagram for this material, is...

Homework Statement find volume of the region bounded by x^2+2y^2=2;z=0;x+y+2z=2 The Attempt at a Solution I figure "slicing" in the z=0 direction would be the easiest the first issue I am having is the upper bound of z, it definitely seems to be 2 but but it's not making sense...

Homework Statement compute volume below z=x^2+y and above the rectangle R= [0,1]x[1,2] The Attempt at a Solution \int_{0}^{1}\int_{1}^{2} x^2+y dydx \int_{0}^{1} [x^2y+\frac{y^2}{2}]\Bigg|_{1}^{2} dx \int_{0}^{1} x^2+ \frac{3}{2}dx \frac{x^3}{3} + \frac{3x}{2}...

I'm an engineering student, and I'm making a formula for the volume of liquid in a cylinder that is cut in half diagonally. r is the radius, h is the height from the bottom to the top of the sloped flat bottom, and L is the height of the water within the cylinder. So when L = h you would expect...

Homework Statement show rectangular box of given volume has minimum surface area when the box is a cube [gotta show it with partial derivatives to minimize] Homework Equations surface area = 2(wl+hl+hw) volume = whl The Attempt at a Solution so this is the one I would be minimizing...

Why there no change in volume and enthalpy of solution when two components are mixed

I have very large data sets: coins & amount i.e. {10 & 11, 9 & 7, 8 & 9, 4 & 5, 3 & 1} graphed would show greater volume to the left side while {1 & 0, 2 & 3, 2 & 1, 4 & 6, 9 & 10} would reflect greater volume on the right, and {1 & 4, 2 & 3, 12 & 10, 4 & 4, 3 & 2} would reflect a surge in the...

Homework Statement The top of a rubber band bushing is designed to absorb vibrations in an automobile is the surface of a revolution generated by revolving the curve z = (0.5y^2) + 2 for (0<= y <= 3) in the yz plane about the z axis. use the shell method to find its volume...

Question: What volume of a 0.835 M solution of Na2SO4 do you have if there are 0.0534 mol of Na+ present in the solution? What I did: Since we have 0.0534 moles of Na+ ions in the Na2SO4 molecule, I used that for the equation. Since 0.0534 moles is in a 1:1 ratio with Na2SO4 I can conclude we...

Homework Statement according to the model ans, the volime of oxygen produced is 25x 24 dm^3 ... where does the 25 come from ?? or someone can show me other step of getting the ans ? thanks in advance! according to the model ans, the volime of oxygen produced is 25x 24...

Homework Statement A 1-cm3 air bubble at a depth of 141 meters and at a temperature of 4 degrees Celsius rises to the surface of the lake where the temperature is 13.1 degrees Celsius, to the nearest tenth of a cm3, what is its new volume?Homework Equations P1V1/T1=P2V2/T2The Attempt at a...

If a helium-filled balloon initially at room temperature is placed in a freezer, will its volume increase, decrease, or remain the same? The Attempt at a Solution If you decrease the T of a vessel filled with gas, its molecules will have less kinetic energy, and the pressure inside the...

From browsing this website I have formed an opinion that people in here don't like when someone brings up information that they heard in a movie.. Well this is more along the lines of a question that arose from watching a movie.. With Sandra Bullock, forgot the name.. Dialogue went something...

I am no english native speaker, sorry if something is a little confuse. I was swimming, and then I realized that when I let the air go our of my lungs I sink. I though this might be because of changes in the volume of my body while holding air or letting it go. So I hold as much air as I...

1.find tthe volume solid generated by revolving the region bounded y=sqrt x and the ;lines y=1, x=4 about the line y=1 2. using simpson rule witj n=4 to aproximate int from 0 to 1 1 over 1-x power 2 dx

The Volume of an atom comes from its electrons and mass of an atom comes from its nucleons. I don't understand why? Any one can explain it please? Thanks in advance