Volume Definition and 1000 Threads

Homework Statement Show that the surface and volume element on a deformed sphere are \sigma = \frac{\rho^2 \sin \theta}{\cos \gamma} d\phi d\theta, dV = \rho^3 \sin \theta d\phi d\theta, if \gamma is the angle between normal vector and radius vector. Homework Equations n\cdot r = \cos...

Hi all, A happy 2018 for all PF members. I have a question. I am trying to understand some basic principle of thermodynamics. My book tells me tge following: "Heating of a gas at a constant pressure uses more heat as when heating the same gas a constant volume" How do i interpret this? I...

Hi .how can i calculate the molar volume and surface tension of nanoparticles ? shoud i have to calculate? or these parameters is available in tables or sth?

I am struggling to fully grasp the concept of flow work for a non-deformabable control volume. Nearly every source puts it in this way: flow work is the work required to push fluid into and out of the control volume and as such is defined as Pv on a unit mass basis. But how can this work be...

I recently watched a great video demonstrating the floating water bridge experiment: At around 34 sec, you can see an electrostatic discharge before the water bridge forms. I've read that this is due to the electrostatic breakdown of air between the two beakers.This made me curious about the...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] I am taking the free energy as the internal energy of the ideal gas. Then the average internal energy per unit volume is ## \frac { 3 nk_B T } {2 } ##. So, the correct option is (c). Is this correct?

Homework Statement Homework Equations The Attempt at a Solution I don't understand how the solution got its values, not from the tables right? because I couldn't find such value from all of the tables. Since the pressure is less than the saturated pressure at given temperature, it is in...

$\tiny{M2215b.08}$ Find the volume of the solid \begin{align*}\displaystyle y&=\sin (x^2)\\ 0&\le x \le \frac{\pi}{2}\\ \end{align*} about the y-axis ok this looks like a cylindrical Shell solution So I set it up like this,,,,, hopefully $\begin{align*}\displaystyle V&=\int_0^12\pi...

Hello I've been working on a problem that involves finding which reaction order gives a greater conversion for a CSTR over a PFR (Xcstr>Xpfr). I was able to solve the mass balance for each reactor, finding: and Allowing us to equate them. This is where I've been stuck for a while now, how...

Homework Statement One cylinder in the diesel engine of a truck has an initial volume of 640 cm3. Air is admitted to the cylinder at 30°C and a pressure of 1.0 atm. The piston rod then does 500 J of work to rapidly compress the air. What are its final temperature and volume? Homework Equations...

Homework Statement I tried to answer the following questions is about the curve surface z= f (x, y) = x^2 + y^2 in the xyz space. And the three questions related to each otherA.) Find the tangent plane equation at the point (a, b, a^2+ b^2) in curved surface z . The equation of the...

Homework Statement Calculate the volume of 1.00 mol of liquid water at 20°C (at which its density is 998 kg>m3),and compare that with the volume occupied by 1.00 mol of water at the critical point, which is 56 * 10-6 m3. Water has a molar mass of 18.0 g>mol. Full answer please! Thanks...

Homework Statement A sample of 1.60 mol H2 (Cv = 20.5 J K-1 mol-1) at 21°C and 1.50 atm undergoes a reversible adiabatic compression until the final pressure is 4.50 atm. Calculate the final volume of the gas sample and the work associated with this process. Assume that the gas behaves ideally...

Homework Statement z=x^2+xy ,y=3x-x^2,y=x find the volume of the region Homework EquationsThe Attempt at a Solution I graphed y=3x-x^2 and y=x I am confused on which region I use to find the volume. Do I use the upper region or the lower region.

Homework Statement Homework Equations in the pic The Attempt at a Solution why is there an extra "r" in the highlighted line? my attempt: ## \int_0^{2\pi}\int_0^2\int_{r^2}^41\ dy\ r\ dr\ d\theta ## = ##\int_0^{2\pi}\int_0^2\left(4-r^2\right)\ r\ dr\ d\theta## thanks

Homework Statement Homework Equations First derivative=maxima/minima/vertical tangent/rising/falling Volume of a cone: ##~\displaystyle V=\frac{\pi}{3}r^2h## The Attempt at a Solution $$L=a^2+b^2~\rightarrow b^2=L-a^2$$ $$V=\frac{\pi}{3}a(L-a^2)$$...

Homework Statement How to calculate the probability of finding an 1s electron within 1 picometer cubic region located 50pm from the nucleus. Homework Equations The probability of an 1s electron within a spherical volume of radius 'a' from nucleus can be find using the expression...

$\textsf{Find the volume of the solid generated by revolving the region about y-axis.Given the boundares of }\\$ \begin{align*} \displaystyle y&=4x-x^2\\ y&=x\\ \end{align*} Ok, I presume since this is rotated around the y-axis that we have to rewrite the equations in terms of y $y=-(x^2-4x)$...

The question is posted in the following post in MSE, I'll copy it here: https://math.stackexchange.com/questions/1407780/a-question-on-matrixs-eigenvalue-problem-from-eberhard-zeidlers-first-volume-o I have a question from Eberhard Zeidler's book on Non-Linear Functional Analysis, question...

Homework Statement Homework Equations First derivative=maxima/minima/vertical tangent/rising/falling When f'(x)>0 → the function rises The Attempt at a Solution $$V=(15-2a)(8-2a)=4a^2-46a+120$$ $$V'=8a-46,~~V'=0\rightarrow a=5.75$$ But: ##~2a<8,~~V(a=4)=0## So 5.75>4 And: ##~V''=8## so it...

$\tiny{t6.1.1}$ $\text{The solid lies between planes perpendiaular to the}$ $\text{$x$-axis at $x=0$ and $x = 4$.}$ $\text{The cross-scctions perpendicular to the axis on the interval $0 \le x \le 4$}$ $\text{are squrares whose diagonals run for the parabola $\displaystyle f_a(x)=-\sqrt{x}$ to...

Homework Statement Consider a sphere of radius A from which a central cylinder of radius a (where 0 < a < A ) has been removed. Write down a double or a triple integral (your choice) for the volume of this band, evaluate the integral, and show that the volume depends only upon the height of the...

Hey Guys! I need some help for solving question 2 of this example as my HSC exam is in 5 days and I want to be able to solve this question if I receive it on the paper. Question: Graph: Answer for Q1 (Just the formula) : Work I have done towards this question: I have realized that from...

Homework Statement Question: https://imgur.com/a/8rUw1 Graph: https://imgur.com/a/Z1oBO Homework Equations Answer for Q1 (Just the formula) : https://imgur.com/a/uesqN The Attempt at a Solution I have realized that from 1-2, there is an increase in pressure, decrease in volume and increase...

Hey! :o I want to draw the space $D$ that is between the paraboloid with equation $z=x^2+y^2$ and the cone with equation $z=\sqrt{x^2+y^2}$ and I want to calculate its volume. How does $D$ look like? To calculate the volume we have to calculate the integral $\iiint_D dxdydz$. I have done...

I'm trying to understand why $$\left(\frac{\partial P}{\partial T}\right)_V = -\left(\frac{\partial P}{\partial V}\right)_T \left(\frac{\partial V}{\partial T}\right)_P$$ where does the minus sign come from?

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > How to find volumeof irregular and porous material like sponge?

The problem is, find the surface area of the volume of revolution generated by rotating the curve y=e2x between x=0 and x=2 about the x-axis. Here's what I have so far... SA=∫y√(1+y2)dx =∫e2x√(1+4e4x)dx and from here I'm not really sure what to do. Any help would be appreciated.

Homework Statement Consider the parallel plate capacitor(no figure). The capacitor plates have a separation distance d in the z-direction. The volume charge density is given by ρ_v. Find v(z).Homework Equations ρ_v = ρ_o*sin(pi*z/2*d) The Attempt at a Solution [/B] ∫(ρ_vdz) =...

What is the surface area ("surface volume") of a 3-sphere having a radius of 2 Planck lengths? Is the product of the Planck's constant, Einstein's proportionality constant and Planck time also equal to this volume? Does this equivalence signify anything? What does it signify?

$\tiny{15.4.17}$ Find the volume of the given solid region bounded below by the cone $z=\sqrt{x^2+y^2}$ and bounded above by the sphere $x^2+y^2+z^2=128$ using triple integrals $\displaystyle\int_{a}^{b}\int_{c}^{d} \int_{e}^{f} \,dx\,dy \,dz$ not real sure where to to start with this?

Hello, I've been watching too much anime. I know that isn't the best way to ask a question scientific in nature, but visualizing bizarre situations is one of the best ways to come up with interesting questions. Anyways, in order to break a rock by compressing it with your hands, you would need...

Homework Statement Problem is given in this image, https://gyazo.com/454370ff9549dcd7c53604ebfe5df105 Homework Equations Continuity or conservation of mass equation: \frac{\partial u}{\partial x} + \frac{\partial w}{\partial z} = 0 Where u is the horizontal velocity and w is the vertical...

Homework Statement Consider a ring of radius R placed on the xy-plane with its center at the origin. A total charge of Q is uniformly distributed on the ring. a) Express the volume charge density of this configuration ρ(s,Φ,z) in cylindrical coordinates. b) Express the volume charge density of...

1. Question Statement and details : 500 mL of 56V H2O2 is kept in an open container due to which some H2O2 is decomposed and evolves 8gm O2 simultaneously, during the process some H2O also vapourizes.Due to all these changes final volume is reduced by 20%. Find final volume strength of H2O2...

Hello everybody!How can I calculate the volume of gasses produced by electrolysis of an aqueous solution of NaNO3 if the mass fraction of the salt changed from 40% to 60% (before electrolysis the mass fraction of the salt was 40% and after electrolysis it changed to 60%)? Pressure and...

Homework Statement A constant volume gas thermometer contains a gas whose equation of state is (p+\frac{a}{V^2_m})(V_m-b)=RT and another, of identical construction, contains a different gas which obeys the ideal gas law, pV_m = RT. The thermometers are calibrated at the ice and steam points...

Ok, so i did a physics experiment a few days ago and now i have to do a write up. The question is does the volume of water in the calorimeter affect the efficiency of the immersion heater? Could someone pls explain to me what happens & y? My results showed that as you increase the volume, the...

Compute the volume of the solid bounded by the planes; $x=7, z=y-2, z=-2y-2, z=0, \mbox{ and } z=2$ Another source said the triple should be but Ii thought it should be $dx\,dy\,dz$ $$I = \displaystyle \int_0^7 \int_0^2 \int_{-\frac{z}{2} - 1}^{z+2} dy\,dz\,dx = 63$$ Hopefully this is the...

This comes from the Intro Homework to my AP Physics 1 class. The teacher said that it is more important to figure out how to use the website than get the correct answers to the questions. However, I want to know how to get the correct answer, especially since I took chemistry last year and...

I was analyzing the Lamborghini Aventador's tech. specs. and it is given Bore x Stroke 95mm x 76.4mm and compression ratio 11.8:1. Then I calculated the volume of displacement and it's 541.5 cm^3 for each cylinder. Then I know the compression ratio as $$\frac{V_1 + V_2}{V_2} = C.R$$ $$...

Homework Statement A sphere of radius 6 has a cylindrical hole of radius 3 drilled into it. What is the volume of the remaining solid. The Attempt at a Solution [/B] I am able to solve this using cylindrical coordinates but I'm having trouble when I try to solve it in spherical coordinates...

If an ideal gas is leaking from a fixed volume, does the temperature of the air in the fixed volume go down, or does it remain constant? We do pressure decay measurements under choked leakage flow conditions, but I wonder if our assumption of constant temperature for the gas remaining in the...

Say you have a rectangular channel with a width, w (m), and a height, h (m) and an infinite length. The channel itself is fixed and none of the sides can move with respect to one another. If you know the volume flow rate, V (m3/s) of fluid through the channel, how do you calculate the shear rate...

Suppose if we have a cube: The volume of the cube is the product of the length, width and the height. All this time, I've been looking at it as: To get the volume, multiply the area of the cross section of the cube by how many "layers" it has. To elaborate with the diagram given, one can see...

Homework Statement The volume of a parallelepiped defined by the vectors w, u, \text{ and }v, \text{ where } w=u \times v is computed using: V = w \cdot (u \times v) However, if the parallelepiped is defined by the vectors w-u, u, \text{ and }v, \text{ where } w=u \times v instead, the volume...

Homework Statement What is the molality of 1M NH4OH dissolved in 70.092ml of water? What is the total mass of the solution? What is the total volume? What is the concentration percent? What is the molar concentration? 1M NH4OH = 35.046g density of water = 1g/ml density of NH4OH = 0.88 g/ml...

I have a work related question. Although it seems like a relatively simple question, I am having difficulties finding the correct equation(s) to calculate the answer. Question: Given a fixed volume air tank filled with pressurized air, how does one calculate the flow rate over time through...

Homework Statement Two ideal van der Waals fluids are contained in a cylinder, separated by an internal moveable piston. There is one mole of each fluid, and the two fluids have the same values of the van der Waals constants b and c; the respective values of the van der Waals constant ''a'' are...

Homework Statement One mole of an ideal gas is warmed slowly, so that the pressure and volume go from (Pi, Vi) to (3Pi, 3Vi), in such a way that the pressure is analogous to the volume. a) What's the Work (W)? b) What is the correlation between the temperature and the volume during that...