Volume Definition and 1000 Threads

Hello, I am working on the derivation that proves that the partial molar volume of an ideal gas is equal to the molar volume of an ideal gas. I am following up to the point in the textbook where they set (∂n/∂ni)nj = 1 where ni is the number of of moles of species i, and nj is the...

If you have a charged solid sphere with uniform volume charge density ρ, then the total charge on the sphere is Q = ρ*4/3*∏*R^3 , where R is the radius of the sphere. Now...

Homework Statement I know how to apply the linear momentum equation for the control volume, but I am not sure why the V2 (velocity of flow from section 2) is V*cos(60). The only reason I can see is the velocity being constant. And since there are two outlet with equal area, the velocity is...

Hi, Sorry for the semi-book here I am working on a project where I am mixing h-BN nanoparticles into a polymer resin to try to tailor the thermal conductivity and dielectric strength of the resulting composite. Admittedly I am not very well versed when it comes to materials science...

Hi, I just need these solutions checked. Thank you in advance! Consider the region bounded by the following curves ##y=x-3, y=5-x, \text{and}\ y=3##: 1.) set up an integral expression that would give the area of the region of y as a function of x: ##y = x-3 = 5-x## ##x + x - 3 -...

Homework Statement Let V be the volume of the solid enclosed by the sphere x^2 + y^2 + z^2 - 2z = 0 , and the hemisphere x^2 + y^2 + z^2 = 9 , z ≥ 0. Find VHomework Equations Using spherical coordinates: x^2 + y^2 + z^2 = ρ^2 z = ρcos(ø) The Attempt at a Solution So I changed both of them to...

I'm having some trouble with this problem: Find the volume of the solid of revolution, or state that it does not exist. The region bounded by f(x)= 6(4-x)^(-1/3) and the x-axis on the interval [0,4) is revolved avout the y-axis. How would I be able to tell whether to use the shell, disk, or...

Find the volume of the solid of revolution, or state that it does not exist. The region bounded by f(x)= the square root of ((x+3)/(x^3)) and the x-axis on the interval [1,infinity) is revolved around the x-axis. I tried using the disk method: pi* (sqrt(((x+3)/(x^3)))^2 Then I think I have to...

Homework Statement Find the volume of the solid generated by rotating the region enclosed by y=\frac{1}{1+x^2} , x=-1,x=1 and y=0 about the line y=2 Homework Equations pi(outer radius)^2-pi(inner radius)^2 The Attempt at a Solution Since i am rotating around a horizontal line i figured...

Homework Statement f(x)=\frac{1}{81}*x^4-\frac{5}{9}*x^2+4 The tangent in Point P(6|0) when rotated around the y-Axis gives the Shape of the Squeezer. The bottom is at y=-5, the top at y=0 The Attempt at a Solution First I calculated the tangent and got t: y=4x-24 Then I converted that to...

I can compute the area of the rectangle formed by Δx and Δy simply by product ΔxΔy. Now, how can I to compute the area in gray given Δr and Δθ? Also, I can to compute the volume of a parallelepiped formed by Δx, Δy and Δz, simply multiplicand ΔxΔyΔz. But, how can I compute the volume...

A cone's volume with height ##x## and radius ##y## is ##1/3## of the volume of a cylinder with height ##x## and radius ##y##.I was trying to visualize it in my head and struggled a bit.Take a rectangle triangle with height ##x## and the other side of length ##y## which isn't the hypothenuse ...

A cylindrical container of height 1 m and diameter 0.5 m is partially filled with apple juice. When the container is lying on its side, the juice level at the deepest point is 37.5 cm (three eighths of a meter from the bottom of the cylinder is full). What is the liquid level after the container...

Homework Statement The surface of a double lobed cam are modeled by the inequalities: \frac{1}{4}\leqr\leq\frac{1}{2}(1+cos2θ) and -9/(4(x2+y2+9)) ≤ z ≤ 9/(4(x2+y2+9)) Find the volume of the steel in the cam. Homework Equations The Attempt at a Solution I know I...

Homework Statement Set up an integral to find the volume of the tetrahedron with vertices (0,0,0), (2,1,0), (0,2,0), (0,0,3).Homework Equations The Attempt at a Solution My method of solving this involves using a triple integral. The first step is deciding on the bounds of the triple integral...

Im confused by a concept i have run across in Griffiths electrodynamics. E_{out} - E_{in} = \frac{\sigma_{free}}{\epsilon_0} However, in the case of a uniform, circular charge density, \vec{E_{in}} = \frac{\rho r}{3\epsilon_0}\hat{r} \vec{E_{out}} = \frac{\rho R^3}{3\epsilon_0...

Hello Homework Statement Show that for an ideal gas: n(E)dE=2πn/(kπT)3/2 *E1/2 exp(-E/kT) dE where n(E) is the number of particles for each element of volume whose energy is between E and E+dE Homework Equations The Attempt at a Solution Really don't know where to start...

This question has been bugging me and the more I think about it the more confused I get. N2O4 ⇔2NO2 Question: the reaction will shift to the right with all of the following changes except A. Addition of N2O4 B. an increase in volume at constant pressure C. A decrease in pressure at...

Homework Statement Find the volume of the solid generated by revolving the region bounded by the parabola y=x^2 and the line y=1 about the line y=1 Homework Equations V= integral of pi*r^2 from a to b with respect to variable "x" The Attempt at a Solution pi(integral of 1-(x^2-1)^2...

Homework Statement A box that is open at the bottom is lowered into the sea (density like water). The outer volume of the box and the air inside it is V_{out}=3 m^3. The moment the box touches the sea surface the air inside it gets trapped and has a volume at V_0=2.5 m^3 and a pressure at...

Homework Statement Find the volume of the solid formed by revolving the region bounded by f(x) = 2-x^2 and g(x) = 1 about the line y = 1. Homework Equations V = ∏∫(1-f(x))^2dx - ∏∫(1-g(x))^2dx The Attempt at a Solution I keep ending up with ∏∫(1-(2-x^2))^2dx - ∏∫(1-1)^2dx, on...

Hello. Homework Statement Basically I want to evaluate the integral as shown in this document: Homework Equations The Attempt at a Solution The integral with the complex exponentials yields a Kronecker Delta. My question is whether this Delta can be taken inside the integral...

Problem: Suppose in a tetrahedron ABCD, AB=1; CD=$\sqrt{3}$; the distance and the angle between the skew lines AB and CD are 2 and $\pi/3$ respectively. Find the volume of tetrahedron. Attempt: Let the points A,B,C and D be represented by the vectors $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$...

Homework Statement Find the volume of the solid bounded above by the surface z = x^2 + y^2 and below by the triangular region in the xy-plane enclosed by the lines x = 0 , y = x , and x + y = 8. Homework Equations V = ∫∫ Height Base The Attempt at a Solution I first found...

I found this matrix in the wiki: https://fr.wikipedia.org/wiki/Vitesse_ar%C3%A9olaire#.C3.89valuation_en_coordonn.C3.A9es_cart.C3.A9siennes I think that it is very interesting because it express d²A not trivially as dxdy. So, I'd like of know if exist a matrix formulation for volume...

what are the dimensions of rectangular beam of volume maximum that can be cut from a trunk in diameter "D" and length "L", assuming that the trunk has the shaped of a straight circular cylinder shape? Answer Width =lenght

The sum of the length and the perimeter of base of a postal package to is 60 cm. find the maximum volume: when the package is cylindrical. The answer is 2547 cm3 V cilinder = pir2h and the sum L + L+H = 60 2L + H = 60 solving for H and putting it into the volume i don't get the answer Yeah...

Consider a sheet of length L and width W. Each corner is cut out (x by x corners removed). Detemine the value of x so when the corners are removed and flaps folded up, the five sided box formed will have maximum volume. SA \(= 1LW + 2 LH + 2WH\) and V \(= LWH\). I am not sure how to do this...

A tree trunk is shaped like a truncated cone it has 2 m of length and diameters of their bases are 10 cm and 20 cm. Cut a square straight section so that the axis of the beam coincides with the axis of the truncated cone. find the beam volume maximum that can be drawn from this form. answer...

I am trying to find the volume of a pyramid where the base has length \(L\) and width \(W\), and the pyramid has height \(h\). Let \(L\) be on the x-axis and \(W\) be on the y axis. In the x-z plane, we have the line \(z = -\frac{h}{L/2}x + h\), and in the y-z plane, we have the line \(z =...

Homework Statement Find the volume of an object bounded by x2 + y2 ≤ 1, x2 + z2 ≤ 1 and y2 + z2 ≤ 1. Homework Equations The Attempt at a Solution This stuff is very new to me (multiple integrals to find volume) so I am not entirely familiar with it. My first thought was to put...

Homework Statement Use cylindrical shells to find the volume of a torus with radii r and R. Homework Equations V= ∫[a,b] 2πxf(x)dx y= sqrt(r2 - (x-R)2) The Attempt at a Solution V= ∫ [R, R+r] 2πx sqrt(r2 - x2 - 2xR + R2) dx I feel like this isn't going in the right direction...

Hello! I just found this website and it looks amazing! I'm not a scientist or anything, but I love it (should've studied physics but oh well), so I think it will be fun and useful for me to join this forum. I am trying to solve a situation, where I'd like to know how much energy would be...

My E&M professor brought up this problem of considering a uniform charge density, rho, that is infinite in volume and then using Gauss's Law to find the electric field at a point. It's resulted in a lot of head scratching and I'd appreciate some help/discussion to guide me towards a resolution...

1. At Lagoon, there is a large granite rock ball that is supported by water pressure, so people can spin the rock. The diameter of the rock is 1.3m. Granite has a density of 2691kg/m^3. Let’s assume a water pressure if 50 lbs/in^2. Calculate the area of the ball that must be in the water...

So, I have this question, but I have no idea what constraint is and how to find a constraint for the length, height and width... and if i say the square wastage is x, then the width is 80-x but I don't know what the length would be with respect to x... , and how do we determine the dimensions..?

Homework Statement Homework Equations The Attempt at a Solution I understand what the question is asking. Both ways I should get the same answer. I'm having trouble figuring out the mathematics behind this question.

Homework Statement The problem is attached in this post. Homework Equations The problem is attached in this post. The Attempt at a Solution Disk method with the radius equal to x/((x^2+3)^5/4) For Trig Substitution √(x^2+a^2) -> x=atanθ a=√3 -> a^2=3 x=√(3)tanθ -> dx=√(3)sec^2(θ)...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement Find the volume of the solid of revolution obtained by rotating the area bounded by the curves about the line indicated. y=x2-2, y=0 about y=-1. Need only consider part above y=-1 Homework Equations V=∏a∫b[f(x)]2dx The Attempt at a Solution I'm mainly unsure of...

When we way that \frac{d^3p}{p_0}=\frac{d^3p}{\sqrt{m^2+\vec{p}^2}} is the invariant volume element, is that with respect to all Lorentz transformations or just proper orthochronous Lorentz transformations?

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement The problem is attached in this post. Homework Equations The problem is attached in this post. The Attempt at a Solution I've set up the integral via disk method: π∫(e^√x)^2 dx from 0 to 1 I've done integration by parts by don't know how to integrate the...

what volume does the "v" in pv denotes? say that in a system where pressure is constant Mg reacts with O2.when dealing with above reaction thermodynamically, HI=UI+PVI where H is the initial enthalpy of the system UI is the...

I am thinking about how to find the volume rotate around its function.Let f be a function of x in the interval [a,b] . The function could be any curve. And the curve is rotation around itself. Would there exist a volume of the curve? And how to find the volumeThank you CBARKER1

Hi! I am trying to make a one-dimentional simulator for two-phase flow. I am going to use the finite volume method, because it is conservative and thus it's easier to keep track of the oil/water ratio in the area. Say you have a conservation equation on the form \nabla \cdot (k(x) \nabla P(x))...

Hi all, I read The unit cell is the smallest structure that repeats itself by translation through the crystal. Some says premitive unit cells contains atoms only at the corners while a unit cell may contain extra atoms in between(like bcc or fcc). At one place I found this: For each...

Hello all, I am a newbie to this site and have found some interesting discussions herein, so I thought it worthwhile asking the collective wisdom of this group about Hygroscopic liquid calculations that I am struggling to correlate. It has been several years now since I worked as an electronics...

Need someone to verify that my work is correct please. Consider the region bounded by $y = sin(x)$ and the x - axis from $ x = 0$ to $x = \pi$ a) Find the volume if the region is rotated about the x - axis. V = \int \pi (sin(x))^2 \, dx \pi \int^{\pi}_0 sin^2x \, dx \pi \int^{\pi}_0...

I have the pipe size, flow rate, and a duration. How can I figure out the amount of fluid that was released from the pipe?