Volume Definition and 1000 Threads

Hi. If an ideal gas of ##N## particles is allowed to expand isothermically to double its initial volume, the entropy increase is $$\Delta S=N\cdot k_B \cdot \log\left(\frac{V_f}{V_i}\right)=N\cdot k_B \cdot \log\left(\frac{2V}{V}\right)=N\cdot k_B \cdot \log\left(2\right)\enspace .$$ This can...

Homework Statement Express volume expansivity (B) in terms of density (ρ) and its partial derivatives Homework Equations B = (1/V) (dV/dT) V = m/ρ The Attempt at a Solution I have only managed to substitute m/ρ into the expansivity equation. Don't really understand how to manipulate the...

Hi guys, 42 year old engine hobbyist here, not a student. I've had great luck figuring out my questions in this portion of the forum in the past and look forward to your input. Keep in mind that I'm not formally educated, so if it's possible to dumb something down a bit I'd appreciate it.1...

Hello everyone, 1. Homework Statement Question : Find the volume of the region which remains inside the cyclinder x 2 + y 2 = 2y, and is bounded from above by the paraboloid surface x 2 + y 2 + z = 1 and from below by the plane z = 0 Homework Equations The Attempt at a Solution This looks...

Hey ! i am having this question to be answered , i am new to the cosmology studies and still a bit confused about some formulas. the question is: (a) The greatest redshift known corresponds to the cosmic microwave background (CMB, CBR) at redshift z 1100 (although the redshift is obtained...

$\tiny{s6.793.12.4.33}$ $\textsf{ Find the volume of the parallelepiped determined by the vectors, a b and c}$ $ a =\langle 6, 3, -1\rangle \, b =\langle 0, 1, 2 \rangle \, c =\langle 4, -2, 5 \rangle $ $\textsf{The volumn of the parallelepiped determined by the vectors }\\$ $\textsf{ $a...

We know that for a closed system, isobaric heating decreases the humidity and isothermal compression increases the humidity. But assuming that we start with the volume completely filled with humid air, is it not true that any increase in temperature must also increase the pressure? If so...

Question: Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y2 = x; x = 2y; about the y-axis Solution...

Hello folks and happy holidays! So I have a theoretical physics question for everyone, I am simply very interested in this subject and would like to know more about how to find, mathematically speaking the force required to create an indentation of a certain size in an object based on known...

Homework Statement We are given a Banana, and asked to find the volume and surface area of the function, using calculus. So far, we have learned elementary calculus (derivatives, limits, and integrals) as well as volumes of revolutions. We traced the banana on graph paper, plotted points on the...

How a klein bottle has a 0 volume? I am a 12th grade student and i don't know anything about topology,klein bottles but i am curious to know how something which exist has a 0 volume. I just watched clifford stoll's klein bottles video on numberphile and i came here to know how a klein bottle has...

Mod note: Misplaced homework moved from General Physics, hence formatting template not shown Beginner here: Was recently given a homework problem: You have a scale (any kind), 2L beeker of water, a series of calibration weights, and one empty juice box. You want to accurately measure the...

Fig.(1) shows a slab whose volume V is given by V = xyz. If the width, the length and the height of the slab, each increases by 1%, what is the increase in its volume?

Homework Statement A six-cylinder four-stroke internal combustion engine, running at 2,200 rpm, outputs 120 kW of brake power. The stroke is equal to the bore. The brake mean effective pressure is 5.5 MPa. Calculate the torque, total displacement volume, stroke and bore. Homework Equations...

Homework Statement Three identical balls fit snugly into a cylindrical can: the radius of spheres equals the radius of can, and the balls just touch the bottom and the top of the can, If the formula for the volume of a sphere is V = 4/3 PI * radius * radius * radius, what fraction of the...

Hi, a water tank will be put in the third level floor or slab. What must be the volume if gravity tank will be used so the pressure would be strong at 2nd floor and ground? It will be primarily a wet fire system. The tank won't be used for any other water applications since the building already...

The volume form on the unit sphere ##S^{n}## in ##\mathbb{R}^{n+1}## is given by $$i_{{\bf r}}\ dx^{1}\wedge \dots \wedge dx^{n+1}=\sum (-1)^{i-1}x^{i}dx^{1}\wedge\dots \widehat{dx^{i}} \dots \wedge dx^{n+1}.$$ Why must the volume form ##dx^{1}\wedge \dots \wedge dx^{n+1}## act on the vector...

Homework Statement [/B] Volume charge density in some space is given by a function ##ρ_v(x)=-ρ_0\frac{x}{a}e^{\frac{-x^2}{a^2}}## where ##ρ_0, a## are positive constants. Determine the electric field vector in arbitrarily chosen point in space. Homework Equations 3. The Attempt at a Solution...

Hey guys had a midterm yesterday but I got stumped on a question with really no idea how to solve it, I'm not really looking for an answer more of a what steps to solve this sort of question. I don't remember exactly what the question was but it was along the lines of Na2CO3 nH2O (This isn't the...

Dear All, I have a question regarding compressed gas. I'm doing some experiment for testing some seal (see hatch area on sketch below) at 10,000PSI by using nitrogen gas. in this experiment, i accidentally got some different result based on two different situation. you can see my experiment...

Homework Statement Find the volume of solid bounded below by plane z = 0 , and above by z = 10 , sides by (x^2) + (y-1)^2 = 1 .. Homework EquationsThe Attempt at a Solution I fins the area of the base first , which is pi (1^2) = pi , then i integrate with the length , which is from z = 0 to...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] So here's my question again, why do you need to include 40L of water in the total volume? It's not like AgCl is going to dissolve in water right? AgCl has low solubility in water. I mean if it was like NaCl then you should...

Hi, I am doing a project for school where I am calculating at what height a balloon would pop from pressure while rising. At the point I am now, I have the initial pressure and the pressure it would pop at. I know work = pressure * change in volume, and that at some point I will need to use the...

Homework Statement A 69.5 kg man floats in freshwater with 2.95% of his volume above water when his lungs are empty, and 4.75% of his volume above water when his lungs are full. Calculate the volume of air, in liters, that he inhales (this is called his lung capacity). Neglect the weight of air...

Homework Statement Suppose W is the region inside the cylinder x^2+y^2=a^2 and inside the sphere x^2+y^2+z^2=b^2, where 0<a<b. Set up an iterated integral for the volume of W Homework Equations x^2+y^2+z^2=b^2 x^2+y^2=a^2 0<a<b The Attempt at a Solution I converted to cylindrical coordinates...

Homework Statement We have an infinite cylinder that, from radius 0 to a, has a volume current density ##\vec{J(r)}=J_{0}(r/a) \hat{z}## , then from a to 2a, it has a material with uniform linear magnetic permeability ##\mu=(3/2)\mu_0## , and at the surface, it has surface current...

Homework Statement What volume in dm³ of KCl is obtained in the following equation 2KClO3-----> 2KCl + 3O2? Homework Equations None The Attempt at a Solution I suppose there is not enough data and according to equation it is 44.8dm³. But my book says 2 dm³, I don't understand how?

Homework Statement Find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic cylinders: y = 1 − x2, y = x2 − 1 and the planes: x + y + z = 2 4x + 5y − z + 20 = 0 Homework Equations ∫∫f(x,y) dA The Attempt at a Solution So I solved for z in the plane...

Are there any general guidelines or rule of thumb regarding how much power in watts would be required to pressurize a cylinder to a particular pressure and can I use this as a general rule, For eg. I want to pressurize a vessel of volume 1 cu. m how much power would be required and can we...

Hi, guys! I came across hard stuff today. I really hope you can help a poor little worm like me. How do you solve for v & T correspondingly for equation like this⇒p = [RT/(v-b)]e^(a/vRT)? What's the technique? How do you call it?

I've just started with statistical mechanics and arrived at the part where they relate entropy to the number of microstates for a given system. The derivation starts of by adding an amount of heat ##\delta Q## to a system and observing the resulting change in internal energy : $$\delta U =...

I remember doing a physics problem over 30 years ago but I can't remember enough to do it again. The only reason I remember it is that it seemed like it would be so useful when I had teenage kids. Funny how the brain works sometimes. Got teenagers now. We were working on acoustics. If I...

Homework Statement : [/B] The density of the Earth's atmosphere varies with altitude, and can be approximated by an exponential: ρ(h)=ρ0e^(-h/h0) where ρ0 = 1.3 kg/m3 (the approximate density at sea level) and h0 = 8.2 km (this is determined empirically). Calculate the mass of 15 km of the...

Hello Everyone, I need to find the volume of this solid bounded by the paraboloids z=x^2+y^2 and z=8-x^2-y^2. I need to find the region of integration. I need to find the limits of integration as well. I tried to graph the two surfaces. Thanks Cbarker1

Find the volume of the following solid: The solid lies below the surface z=x^3y and above the triangle in the xy plane with vertices (1,0), (2,1) and (4,0). The region is graphed (1,0);(4,0);(2,1);I need to find the y limits in the double integral. Thanks CBarker1

Homework Statement In the case of a gas obeying the equation of state $$\begin{align}\frac{Pv}{RT}&=1+\frac{B}{v}\end{align} $$ where ##B## is a function of ##T## only, show that, $$\begin{align}c_v&=-\frac{RT}{v}\frac{d^2}{dT^2} (BT)+\left(c_v\right)_0\end{align}$$ where ##\left(c_v\right)_0##...

Homework Statement When, using a eudiometer in a lab to collect gas over water, if you have to switch eudiometers is the final volume of water displaced equal to the water displaced in the first tube + the water displaced in the second, and would the pressure be calculated through the total...

How can you calculate air volume in cubic feet per minute through a fan when the only data available is pressure drop and fan diameter? For example, How many cubic feet per minute of air is a fan blowing if it has a diameter of 20" and a pressure drop of -50 pascals?

Homework Statement Find the volume of solid which is bounded by z = 4-x-y and below by region in the plane of 0<x<2 , 0<y<1 When i use zx -plane projection , i found that my ans is different with the ans of using xy projection ...Which part i did wrongly ? From the ans given , volume = 5...

Homework Statement Hi, I don't even know where to begin with this type of graph. It does say that the graph should be a straight line. This is for one of my questions for my lab that I am completing. This is the link of mytable with info...

Apologies if this question has already been asked, but is it not possible to derive the formula of a sphere by imagining a circle sliced in two, then rotating this semi-circle about the flat side (imagine the flat side is stuck to a skewer) by 2Pi, so as to sum up the semi-circles to "create"...

$\tiny {205.23} $ $\text{ The volume }\displaystyle V=\frac{4}{3}\pi{r}^{3} \text{ of a spherical balloon changes with the radius.} $ $\text{a) at what rate } \displaystyle \frac{ft^3}{ft} \\$ $\text{does the volume change with respect to the radius when $r=2 ft.$} $...

The question reads, "Find the dimensions of a cylindrical tennis ball container which has the volume of V(x)=8πx3+17πx2+10πx+π such that the volume is exactly 825π cm3. Hint: V = πr2h." To start off, I set V(x)=825π and moved it to the right side, giving 0 = 8πx3+17πx2+10πx-824π. Factoring...

Hi, I am looking for a formula to have the volume of this shape. Here is how we draw it: Thank you for your help :)

This is probably a simple question but I am really struggling as to where to start. We have a tank of compressed air, Volume of tank (V1) = 0.2litres Pressure of tank (P1) = 206.8 bar Regulator Pressure (P2) = 58.6 bar I would like to find the volume of air that can pass through the regulator...

Mt. Vesuvius in Pompeii was a conic volcano with a height from its base 7950 feet and a base radius of 2300 feet. In 79 AD, the volcano erupted, reducing its height to 4200 feet . Find the volume of the volcano after 79 AD in terms of pi. WORK: Volume of Volcano(Before 79AD)= \pi *r^2*h/3...

Homework Statement Lead has a mass of 11.35 g per cubic centimeter of volume, and the mass of one of its atoms is 3.439×10-25 kg. If the atoms are spherical and tightly packed, what is the volume of an individual atom? ( m3) Homework Equations conversions The Attempt at a Solution For this...

Anyone has schematic of remote volume control for stereo amplifier? It has to drive a motorized volume pot, not the digital attenuator type of volume control. Thanks Alan

Homework Statement I am supposed to find the increase in volume, or more specifically how much mercury will rise inside of a thermometer, given the following values. The volume expansion is 1.8 * 10-4/C(degree Celcius). The temperature increase from 30 to 70 degrees F (already converted the...

HOMEWORK POSTED IN WRONG FORUM, SO NO TEMPLATE I have encountered a problem at the university in which there is a thermally isolated container of constant volume in which the number of particles and temperature change with time(the temperature increases). The change in particle number ensures...