Volume Definition and 1000 Threads

I was reading about the Pendle Hill experiment by Henry Power and Richard Towneley showing the relationship between Volume and Pressure in gas that eventually became Boyle's Law. The higher they got the greater the volume became. My question is, was the gas measured in the barometer isolated...

Homework Statement forumlate if its growth/decay is exponential I have equation that i intergrated and found Pressure over volume = work done of pressure P = 3.2c^-1.4 f(v) = -8v^-0.4 i set limits of 10x10^-6 --> 100x10^-6 and 10x10^-6 --> 100x10^-6 but i increase both values by 20x10^-6 every...

Homework Statement [/B] Oceans cover 2/3 of the earth’s surface, with an average depth of 3.7 km. The average surface temperture is 17◦ C. Taking this temperature as representative of the entire ocean, and knowing that the coefficient of volume expansion for water at this temperature is β = 1.7...

Homework Statement a hut has to side walls a roof and back wall. its front is open. its total volume is 120m^3 fdetermine the miniumal surface area necessary for a sheet to be put over it Homework EquationsThe Attempt at a Solution Attempt 2 V=xyz=120 z=120/xy s = 2yz + xz + xy s = 2y(120/xy)...

Hi all, I have been reading Griffiths' book on Electrodynamics and have come across a point (image attached below) where he states that volume current densities are 0 on the surface of the current-carrying objects. He then uses these properties in pretty-important integrals. However, I...

Homework Statement If ##\vec { F } = x \hat { i } + y \hat { j } + z \hat { k }## then find the value of ##\int \int _ { S } \vec { F } \cdot \hat { n } d s## where S is the sphere ##x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4##. The Attempt at a Solution From gauss divergence theorem we know ##\int...

Homework Statement It is necessary to calculate the volume of the coin which has mass 25 kg and how does change its volume when it is necessary to calculate its volume at a depth of 5000m. Compare volume change by pressure with the volume change by pressure with the Volume change by...

Homework Statement the question asks for the concentration of ethanoic acid, therefore I need to find out the volume of ethanoic acid used during the titrations. I thought it would be 30mL because that's when the temperature reaches maximum. But the answer says that the volume should be in the...

My question is, why is the circled integral the chosen integral for this case? My thoughts are that we don't just use ##\int_0^1e^{-x}## because we need to make this two dimensional area into a three dimensional volume by doing 360 degrees of rotation. This would correspond to ##2πr##. ##2π## is...

I want to explain to a little child (4.5 years) what the differences between volume vs. capacity. Can you give me some tips?

I was looking at the following proof of Louviles theorem : we define a velocity field as V=(dpi/dt, dqi/dt). using Hamilton equations we find that div(V)=0. using continuity equation we find that the volume doesn't change. I couldn't figure out the following : 1- the whole point was to show...

In FLP Volume 1 section 17.4, Feynman derives the 4 momentum. He gives the expression for v'(velocity in the moving reference frame) then says to find E' we need to square v', subtract it from one, take the squad root, and take the reciprocal. He does this to get E' is simply mo times the...

Simpsons formula and the volume of a pyramid frustum Normally I consider myself quite adept in mathematics, but I simply lack the right idea and/or the mathematical creativity to solve this assignmenent: "Prove that the Simpsons formula V = 1/6 * h * (Ab + 4Am + At) can be used to calculate...

This paper by Christodolou and Rovelli discusses how to define the interior volume of a black hole: https://arxiv.org/abs/1411.2854 I'll try to condense their basic argument into a (heuristic) form that makes it easier to raise the issues I want to raise. The basic idea is to start with the...

Hi All, I am trying to find out how much CO2 (ppm) would be released into a ventilated room (m3) from a faulty pressurized gas cylinder to calculate risk associated. Would anyone be able to help me with a formula? I was trying to work with V=nRT/P but wasn't sure how do I translate the outcome...

Homework Statement Find the value of the solid's volume given by the ecuation 3x+4y+2z=10 as ceiling,and the cilindric surfaces 2x^2=y x^2=3*y 4y^2=x y^2=3x and the xy plane as floor.The Attempt at a Solution I know that we have to give the ecuation this form: ∫∫z(x,y)dxdy= Volume So, in fact...

I found a simulation tool on wolfram alpha where the pressure of a constant volume is calculated. The pressure is affected by the heating of a mixture of water and air inside the container. There is an explanation to how the pressure is calculated which seems pretty straight forward. But there...

Homework Statement Hello, a bowl is created when rotating the function f(x) = \begin{cases} 0, & 0 \leq x \lt 6 \\ (12/\pi)arcsin(x-6), & 6\leq x \leq 7 \end{cases} around the y-axis. Find the height (h) and the volume (V) of the bowl.Homework EquationsThe Attempt at a Solution So, I graphed...

Homework Statement What volume in milliliters of .500 M HNO3 is required to neutralize 40.00 milliliters of a 0.200 M NaOH solution? Homework Equations The balanced chemical equation HNO3(aq) + NaOH(aq) → H2O(l) + NaNO3(aq) The Attempt at a Solution .200 mol NaOH/1L x 0.04000 L x 1 mol HNO3/...

The ans comes out (c) if I take specific heat at constt volume to be independent of temp. Whether the specific heat is always temp. independent for an ideal gas??

Homework Statement "Find ##P(Y^2>4xz)##, where ##(x,y,z)\in (0,1)^3##." Homework EquationsThe Attempt at a Solution ##P(Y^2>4xz)=P(Y>2\sqrt{xz})+P(Y<-2\sqrt{xz})=P(Y>2\sqrt{xz})=P(1>Y>2\sqrt{xz})## Here, I set the boundaries for integration over this "wedge", for the lack of a better term...

Why isn't it called deltaP *delta V work? Or deltaP*V work? Does the expression mean that P is constant while V changes and also what is an example of that? thanks for any help

Homework Statement This is for a lab report and I am just confused about how I should regard volume because this issue is affecting 3 other questions. If you heat a gas in a closed flask that is connected to a manometer with water in it, the water level goes up (the arm open to atmosphere rises...

Homework Statement Let R be the area in the xy-plane in the 1st quadrant which is bounded by the curves y^2+x^2 = 5, y = 2x and x = 0. (y-axis). Let T be the volume of revolution that appears when R is rotated around the Y axis. Find the volume of T. Homework EquationsThe Attempt at a Solution...

Homework Statement Let C be the parametrised surface given by Φ(t,θ)=(cosθ/cosht, sinθ/cosht,t−tanht), for 0≤t and 0≤θ<2π Let V be the region in R3 between the plane z = 0 and the surface C. Compute the volume of the region V .Homework EquationsThe Attempt at a Solution I thought I needed...

Homework Statement A container with height 4.5 is created by rotating the curve y = 0.5x^2 0 \leq x \leq 3 around x = -3 and putting a plane bottom in the box. Find the volume V of the box. Homework EquationsThe Attempt at a Solution I want to solve this by using the shell method. I have...

Homework Statement Let G be the region bounded by the planes x=0,y=0,z=0,x+y=1and z=x+y. Homework Equations (a) Find the volume of G by integration. (b) If the region is a solid of uniform density, use triple integration to find its center of mass. The Attempt at a Solution [/B] My...

Homework Statement Convert a number concentration of 15 X 10^12 molecule/cm3 into volume mixing ratio at: a) 1 atm pressure, and 20 C temperature. b) 500 mbar pressure, and 253 K temperature. Using the Ideal Gas Law, calculate: a) Loshmidt’s number (# of molecules/cm3 of air, at standard...

Hello! I am studying Zeidler's QFT Volume II, and I have a query on page 808: It is claimed that S Ψ^+_{p,s} = (sk)Ψ^+_{p,s} when p=p^3 k. I tried my hand at deriving this, but when we write S=S^1i+S^2j+S^3k, then the S^3k term acting on Ψ^+_{p,s} does give skΨ^+_{p,s}, but I don't see...

Could one make a negatively-charged insulator with the extra electrons trapped all the way through its volume by building it up layer by layer with electrons "sprayed" onto each layer as it was constructed? I guess the electrons would be trapped in empty atomic orbitals within the material - is...

I am looking for an explicit equation that shows that a sample with lesser volume will reach higher temperatures when irradiated than a sample with a larger volume. The samples in my project are biological tissues which are being irradiated by a laser. In my experiment, using a thermal camera I...

Homework Statement The density of an object is given by its mass divided by its volume: ##p=\frac{m}{V}## Use a calculator to plot the volume as a function of density (##V=\frac{m}{p}##), assuming a mass of 8kg (m=8). In the follow-up question (part b): Evaluate ##\lim_{p \rightarrow 0}...

Homework Statement Hi guys. So for my biology class, we were doing a water chemistry experiment. We placed potato cells into beakers of different [sucrose] (dissolved in water). The goal was to plot the change in mass % on a graph, make a linear trendline, and see which solution was isotonic...

Can we say that a volume element can be represented by a vector, or is there some hidden complication that makes this inadvisable? For some background, the stress-energy tensor has been described as the density of energy and momentum, in for instance MTW. So if one says that the represention...

So, let me preface by saying I’m neither a scientist nor a mathematician, so am requesting some talented help here checking the accuracy of my source information and math. Regarding star formation, I got curious about how much volume of space in the interstellar medium is actually required to...

Hello everyone, Is there a proof that takes us from the sum idea of the volume: $$\sum_{i=1}^m \sum_{j=1}^n f(x_i,y_j) \Delta x \Delta y$$ To the integral idea: $$\iint_R f(x,y) dxdy$$ Or something that relates the volume to the integral just like The Fundamental Theorem of Calculus?

Homework Statement Derive the volume of sphere using Calculus. i saw videos on this topic on youtube, but i want to do it by the method of integrating a circle at angle θ (Theta) . i am posting a photo where i explained every thing i did but i couldn't know what i am doing wrong. Homework...

Let $E$ be the set of all real $4$-tuples $(a, b, c, d)$ such that if $x, y \in \mathbb{ R}$, then: $(ax+by)^2+(cx+dy)^2 \le x^2+y^2$. Find the volume of $E$ in $\mathbb{R}^4$. Source: AMM.

I'm trying to figure out how the finite volume version of Lax-Wendroff scheme is derived. Here is the PDE and Lax-Wendfroff scheme, assume initial conditions are given: $$u=\text{function of x,t}\\\hat{u}=\frac{1}{\Delta x}\int_{x_{i-1/2}}^{x_{i+1/2}}u\thinspace dx \text{ (the average flux...

Hi. Please excuse my ignorance but this entire volume translation formulas for EOS confuses me to no end. Could someone tell me how the volume-translated Peng-Robinson exactly works? How do I calculate the fugacity expression of VTPR? Do I integrate the V + c terms against dV or do i integrate...

Xinyi used 2 bottles of mango syrup and 9 litres of water to make a mango drink. There were n litres of mango syrup in each bottle and she then pouredthe mango drink equally into 20 glasses. a) What was the volume of mango drink in each glass? Give your answer in terms of n. my answer...

THE QUESTION By using Riemann’s sum, synthesise a mathematical model for finding the exact volume of any ‘tepee’ tent of side s and height h. HERE'S WHAT I HAVE Am currently stuck on writing a side length for the hexagon at any height 'x'

I am looking to prove or disprove the following statement: Two objects, of the same homogeneous material, the same mass, the same volume, the same center of mass and the same moment of inertia will be dimensionally the same. If there is a way to generate a mathematical proof, that would be...

First off, this is not a homework question nor assignment. I'm working on building a solar shower to mount on my car out of PVC, and don't feel like pumping large volumes of air with a bike pump. I'm looking at a portable air pump, or compressed gas in a tank with a regulator (and blow off...

The main aim of my question is to find time taken by gas filled tank while emptying (from full to zero) it into atmosphere? I require a set of equations which might be used in the calculation of such a situation. Known parameters are: 1. Pressure inside the gas tank. 2. Dimension and shape of...

This is what i have so far We can find the exact volume of any shape using: V= int[a,b] A(x) dx Where,A(x)is the cross-sectional area at height x and [a,b] is the height interval We know that the horizontal cross-sections are hexagonal ∴A=(3√3)/2 a^2 Where a,is the length of a side Write the...

Homework Statement If mole fraction, pressure fraction and volume fraction are denoted by Xmol , Xp, XV respectively, of a gaseous component, then what is the relation between them? Homework Equations mole fraction = mole of component / total moles pressure fraction = pressure of component /...

Homework Statement We know that one mole of any gas occupies 22.4 L at STP. But I am a little confused because if I increase the volume of the container then the volume will also change, but how is there a fixed value of 22.4 L? Homework EquationsThe Attempt at a Solution I reasoned it out as...

Homework Statement Consider a perfect monoatomic gas at pressure $p_i$ 1.2 atm and temperature $T_i$ 300K, that is in equilibrium inside a cylinder having a volume $V_i=1L$ and which piston has a mass of 1kg and is at an height of 50 cm. Admit that a mass M=3.13kg is over the piston. When that...

My understanding is that the amount of heat energy a parabolic reflective surface generates is not the volume of surface area of the mirror, but essentially the volume of surface exposed perpendicular to the suns rays. This effective surface can be also described as the area of shadow that is...