Volume Definition and 1000 Threads

In my textbook, it says that pV=C (Boyle's Law), V/T=C (Charle's Law) and that P/T=C (pressure Law). The problem is that I cannot see how the first two equations combine to give the last one. If I divide the first equation by the second, I get that pT=C, which certainly is not the same as the...

Homework Statement There is a vessel with 10 Liters of Liquid Nitrogen. The normal pressure is 100 Psi. After a couple hours the pressure is dropped to 47 Psi because of leak in the vessel. How much of the Liquid Nitrogen did we lose/is left in the vessel? Homework Equations I'm really not...

Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=http://msr02.math.mcgill.ca/webwork2_files/jsMath/fonts/cmsy10/alpha/144/char70.png...

Okay, so this is quite hard to explain in words so I will use pictures. Suppose you have a Square with the length of W You also know the distance from the pink surface to the center of the square is X. The rotation of the square is theta. As shown in the picture above... So the problem is: Is...

Hey everyone, I was recently reading a paper on surface enhanced Raman scattering, and it mentioned that plasmons (and for that matter surface plasmon polaritons-where my interest lies) are sensitive to the surface to volume ratio of the structure. I can begin to understand intuitively with...

hi guys, this is the first time i post a thread. I have an issue on proving the scalar products for arbitrary momenta. Can anyone help me ? I always end up with N(p)N*(p')(D(L^-1(p)L(p'))_rowrow'detla I have been spending hours on proving this..still i can't prove it...

Homework Statement Evaluate: \int_{0}^{a} \int_{0}^{b} e^{max(b^{2}x^{2}, a^{2}y^{2})} dy \hspace{1 mm} dx Where a and b are positive. Homework EquationsThe Attempt at a Solution I'm having some trouble getting started with this problem, mostly because I am not very familiar with the...

I'm still confused on some of these volume problems, so please bear with me :) Homework Statement Find the volume of a reentry spacecraft nose cone that has a cross-section radius of (1/4)x2 taken x feet from the nose and perpendicular to the axis of sym. We are given that the length of...

I have a problem for a written assignment in my calc 2 class involving the volume of a cylindrical glass. A cylindrical drinking glass 10 in tall and 4 in in diameter is filled with water, and then tilted so that the water pours out until half the base is exposed. Write an integral to find the...

I have say a 250cm3 liquid with a solid dissolved inside filled in a container. If I pour 50cm^3 of that liquid in another container, would the number of moles of the solid inside the 50cm^3 container be different to the number of moles in the original 250cm^3 container? I've been told the...

Homework Statement Integrate $$\int_V \delta^3(\vec r)~ d\tau$$ over all of space by using V as a sphere of radius r centered at the origin, by having r go to infinity. Homework EquationsThe Attempt at a Solution This integral actually came up in a homework problem for my E&M class and I'm...

Homework Statement Hello, I am to find the volume of the solid given by x2 + (y-1)2=1 rotated about the y-axis. I may use either shells or cylindrical method. I attempted shell method, but am just learning this, still foggy and this is the one question that isn't coming out right. Homework...

I started reading Schwinger's first volume of the monograph: "particles, sources and fields" And I must say it's hard book to read, has anyone read it or wish to correspond here or on PMs about any thing that is being deduced in the book/s? Or am I the only bloke who read this book, besides...

Hello, I am looking at reactions that change volume during the reaction, for example ammonia synthesis N_{2} + 3H_{2} \rightleftharpoons 2NH_{3} where it is clear that the products are less moles than the reactants. However, I am thinking of a scenario in a plug flow reactor where this is...

Homework Statement Suppose that the volume transport associated with the wind-driven circulation's western boundary current (such as the Gulf Stream) is 50 x 10^6 m^3/second. Assume that this volume transport is carried in a current of uniform speed which is 50 km wide and 1 km thick...

Suppose that volume transport of an ocean current is 50 x 10^6 m^3/s. Assume that this volume transport is carried in a current of uniform speed which is 50 km wide and 1 km thick. What is the average velocity of the current? Suppose that the velocity of a current is 0.2 m/s. Assume that...

Homework Statement So we know Enthalpy under constant Pressure and Internal Energy under Constant Volume. By H = U + dPdV U= I + W W= -PdV under Isobaric conditions H = I -PdV + dPdV = U Enthalpy = Internal Energy _________________________________________ Under Isochoric Conditions W= O...

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.