Volume Definition and 1000 Threads

Homework Statement Find the volume of the given solid. Bounded by the planes z = x, y = x, x + y = 5 and z = 0 Homework Equations V =...

NO TEMPLATE BECAUSE THREAD WAS ORIGINALLY ENTERED INTO WRONG FORUM Hi Guys, I have attached the question that I am struggling with (part b of the question) I have worked out that the conversion of A is X=0.21 Using this conversion I'm trying to work out the time required for the reaction I...

Homework Statement Find the volume of a right circular cone with height h and base radius r. Homework EquationsThe Attempt at a Solution I've chosen the case where y = x = r = h. Then, I solve the integral in the image above and I got the book's answer. But is it actually correct?

why can't it be like this?

why change of volume in pure torsion is zero? if you consider stress in plane with degree of 45 there is normal stress normal stress can lead to change of volume

I am wondering if equation $$C_v=(\frac{∂U}{∂V})_T$$ applies only to ideal gases or applies generally for any other system? The second question I have is can we use the following relation: $$dU=nC_vdT$$ in processes that are non isochoric (that is for processes where volume is not constant)? I...

If buoyancy is due to the pressure differential as we go deeper in a liquid, then that pressure differential should depend on the vertical dimension of the immersed object. Eg. if we have a long cylinder vertically placed, the pressure differential between its top surface and its bottom surface...

Homework Statement A car engine moves a piston with a circular cross section of 7.500 ± 0.005cm diameter a distance of 3.250 ± 0.001cm to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume. Homework...

Hi, I recently did an experiment whereby we investigated the velocity distribution of air expelled from a round nozzle whose diameter, D, was 30mm. We have been asked to calculate the volume flow rate at distances of 2D, 6D and 10D along the centreline. We found the flow rates to INCREASE...

Homework Statement A sphere has a diameter of ##D = 2\rho = 4cm##. A cylindrical hole with a diameter of ##d = 2R = 2 cm## is bored through the center of the sphere. Calculate the volume of the remaining solid. (Spherical or cylindrical coordinates?) hint: Place the shape into a convenient...

Homework Statement The Earth's radius is 6371 km. If the Earth's radius were to increase by 30 m (0.03 km), but no change in mass, by what percentage would the Earth's rotational period increase? (Model the Earth as a uniform sphere) Homework Equations ∑Torque = Iα v = rω a = rα KE = (1/2)Iω^2...

Homework Statement [/B] The diameter and depth of an antenna that is shaped like a paraboloid are ##d = 2.0m## and ##s = 0.5m## respectively. The antenna is set up so that its axis of symmetry is at an angle ##\theta = 30^{\circ}## from it's usual vertical orientation. How much can the antenna...

A right circular cone is inscribed inside a larger right circular cone with a volume of 150 cm3. The axes of the cones coincide and the vertex of the inner cones touches the center of the base of the outer cone. Find the ratio of the heights of the cones that maximizes the volume of the inner...

Hi I have a few questions about light-cones. I have read the previous threads related to my question and have a few things to clarify. I have taken two events say p and q . (1+2 D - so that its easier to imagine) CASE A : Flat spacetime Case 1 : If p and q occur at the same place (according...

I'm having trouble understanding the role of the volume of velocity space when deriving the Maxwell-Boltzmann speed distribution. 1. If we wish to compute the speed distribution from the velocity distribution we work with, say, p(v) dv \propto v^2e^{-av^2} dv where the ##v^2 dv## comes from...

What is the equation used to calculate the volume of a four- dimensional "sphere," or hypersphere?

Homework Statement So I am trying to accomplish the above by using spherical coordinates, I am aware the problem may be solved using dv=dxdydz= zdxdy were z is known but I would like to try it using a different approach (using spherical coordinates). Any help would be greatly appreciated...

Homework Statement A volume is enclosed by the plane z = 0 and the inverted paraboloid, z = 6 − r2 (expressed in cylindrical coordinates). Find the volume and its surface area. Hence, using a suitable linear transformation, find the volume of the region enclosed between the surfaces z = ax^2...

Homework Statement Question: For a fluid flowing within a horizontal tube, if the diameter of the tube narrows, will the fluid's flow rate increase, resulting in increased pressure in the narrowing and explain your reasoning. Homework Equations Volume flow rate = volume/time Volume = Area x...

Hello all, I wanted to say thanks to everyone on this forum who dedicate their personal time to enlighten so many like myself. I am a fan of physics and consider myself a student for life. I recently bought an Indoor Air Quality (IAQ) sensor/monitor to test my air purifier and as expected...

Homework Statement Homework Equations Coefficient of water expansion for volume given by the textbook is 207 x 10^-6 The Attempt at a Solution [/B] I did 80.4*0.000207*0.000369 = 0.00000614119 m^3

Homework Statement A circular pond with radius 1 metre and a maximum depth of 1 metre has the shape of a paraboloid, so that its depth z is z = x 2 + y 2 − 1. What is the total volume of the pond? How does this compare with the case where the pond has the same radius but has the shape of a...

Find the volume of the solid generated by revolving the region bounded by y = 4x-x^2 and y = 2x about the y-axis. About the line x = 2. Since this is rotated about the y-axis, I know I have to manipulate the equation so I can get to x = something. The problem is I cannot change the equation y =...

Homework Statement I have the attached problem ,and Show my answer and solution, My answer is 3.14*(15 -8ln4) While book answer 3.14(15+8ln) Can anyone point to the mistake I made?

What are two aspects in which the volume expansion of liquids and the volume expansion of gases due to a temperature change vary? Answer: One of the aspects is that gases can be more easily heated than liquids. This is because there are intermolecular forces (Van Der Waals interactions)...

Hello all, I am not too experienced with geometry. I am just curious whether it would be possible to define a shape based on variables. Say you have a simple relationship between volume and some variables. V=x+y. This tells you about the volume of a 3D object, however, it does not describe the...

Homework Statement If a 5kg object floats in water (density=1000 kg/m3) with 20% of it's volume above the surface of the water, what is the volume of the object? Homework Equations Archimedes' Principle = the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or...

Homework Statement When 0.40 mol of oxygen(O2) gas is heated at constant pressure starting at 0 degrees C, how much energy must be added to the gas as heat to triple its volume? (The molecules rotate but do not oscillate) Homework Equations pV=nRT p1V1/T1=p2V2/T2 Q=mcdT Value of Cp for Oxygen...

Can someone explain in depth ( in simple term) how potential divider is link to adjusting volume and sensors. Please share any digram if it ia helpful for me. Thank you

Homework Statement how to calculate the specific volume in this question ? the author didnt gave the ans though. Should i take the volume displaced by the water or volume of the stone ? the specific volume is given by the formula v= V / m Homework EquationsThe Attempt at a Solution

The question is: A solution contains 23ppm of dissolved O2 in 242.0066 mL of solution. What is the mass of the oxygen. Formula: ppm=(grams of solute/grams of solution)*1,000,000 I tried plugging stuff in but it wasn't working out what so ever. I just don't know how to do these when given so...

Homework Statement Question 1: An insulated 8-m3 rigid tank contains air at 600 kPa and 400 K. A valve connected to the tank is now opened and air is allowed to escape until the pressure inside the tank drops to 200 kPa. The air temperature is maintained constant by an electric heater during...

Hi all, I'm having some trouble figuring out why entropy is used instead of enthalpy for an open system. From what I understand, an open system uses entropy to calculate internal energy. Since the control volume is constant (i.e. Δv = 0), wouldn't using : h = u + PΔv effectively be h = u? So...

Hello! (Wave) I want to find the volume of the parallepiped that has vertices the $(0,1,0), (1,1,1), (0,2,0), (3,1,2)$. In order to find the volume we have to find three linearly independent vectors that span the parallepiped. In order to do this, can we fix any of the given points and...

I'm studynig thermodymamics using the textbook 'Thermodynamics foundations and applications' (Beretta and Gyftopopulos). The definition of a system according to the authors consist in the specification of : -the costituents of the system ( atoms or molecules or prottons neutrons ... in...

Homework Statement A clown at a birthday party has brought along a helium cylinder, with which he intends to fill balloons. When full, each balloon contains 0.00260 m3 of helium at an absolute pressure of 1.10 x 105 Pa. The cylinder contains helium at an absolute pressure of 1.80 x 105 Pa and...

So my question is, if the bulk modulus change by 5%, what is the fractional volume change value? is it times 0.05 or divided by 0.05? or the fractional volume change still the same?

Homework Statement why the formula of volume is given by integral of P and dA , the integral of P and dA would yield Force , right ? Homework EquationsThe Attempt at a Solution

Homework Statement Find the volume of the solid obtained by rotating y=x^2 and x = y^2 about y=2 Homework Equations V= 2πrh The Attempt at a Solution When I had constructed the graph I determined the following: r= 2-(y(1/2)) h= 1-y2 after converting V into an integral I applied fundamental...

Homework Statement A sample consisting of one mole of a diatomic perfect gas is heated from 25 °C to 200 °C at constant volume. Calculate q, w, ΔU and ΔH for the process, given that Cv = 23.02 J K-1 mol-1 . Homework Equations Im studying for mid terms and i have no lecture notes on diatomic...

Mod note: Moved from technical math section, so is missing the homework template. A right triangle the hypotenuse of which is c revolves about a small side. A right circular cone is formed. Find the largest possible volume of the cone. Vcone: pi*r^2*(h/3)I don't get why they mentioned the...

Homework Statement 1 liter of ideal diatomic gas (allow for rotation but not vibration) at a pressure of 1 atmosphere and a temperature of 300 K is compressed adiabatically to a pressure of 7 atm. What is the volume of the gas after compression? Homework Equations PV=NKT PV=nRT ##U_T##=f/2*NKT...

Homework Statement [/B] Homework Equations $$W=P\Delta V$$ $$\Delta U=nC_v\Delta T$$ The Attempt at a Solution . [/B] The gas is slowly heated. The temperature increases and the pressure increases as well. But since volume increases, the increases in pressure is nullified. The process is...

Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=x2 x=y2 Rotated about y=1 Homework Equations Area of cross-section (in this case, a disk) = A(x) = π(outer radius)2 - π(inner radius)2 Volume = V = ∫A(x) dx...

Hi, I have a hard time calculating volume in a closed container. Let's say, I have a flask with a volume 0.125ml, which is closed, and the pressure inside is 16.87kPa with temperature 294.7k and I did some reaction to create a gas inside the flask. The new pressure in the flask is 87.19kPa and...

Homework Statement Find the triple integral for the volume between a hemisphere centred at ##z=1## and cone with angle ##\alpha##.The Attempt at a Solution What I tried to do first was to get the radius of the hemisphere in terms of the angle ##\alpha##. In this case the radius is ##\tan...

Use an appropriate volume integral to find an expression for the volume enclosed between a sphere of radius 1 centered on the origin and a circular cone of half-angle alpha with its vertex at the origin. Show that in the limits where alpha = 0 and alpha = pi that your expression gives the...

Hello, I was wondering if some one would be able to check my thought process on this. I have an object ( a boat) which I'm only able to calculate the tensors of the volume moment around its volume centroid. If i assume that the object has a uniform density ( which it does not, just bear with...

Homework Statement Calculate the volume integral of the function $$f(x,y,z)=xyz^2$$ over the tetrahedron with corners at $$(0,0,1) (1,0,0) (0,1,0) (0,0,1)$$ Homework Equations I was able to solve it mathematically, but still can't figure out why the answer is so small. I only understand...

Homework Statement A person (with mass 60.0 kg) is located on a volume of ice, floating on the water. Calculate the smallest volume of the ice so that the person would remain above the water ( ice density = 917kg / m3)[/B]Homework Equations F= m xg Archimedes F = density x V xg [/B] The...