What is Volume: Definition and 1000 Discussions

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or 3D shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.
Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. Volumes of complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.
The volume of a solid (whether regularly or irregularly shaped) can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of just one of the substances. However, sometimes one substance dissolves in the other and in such cases the combined volume is not additive.In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian invariant.
In thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure.

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  1. B

    Volume of Oxygen Liberated from Hydrogen Peroxide

    Homework Statement Hydrogen peroxide breaks down easily to give water and oxygen as follows: 2H2O2(aq)----> 2H2O2(l) + O2(g) Bottles of hydrogen peroxide are sometimes labelled as 10 volume as well as 3%. This means the volume of oxygen that can be liberated is 10 times the volume of the...
  2. karush

    MHB W9.3.8 volume by rotation

    http://mathhelpboards.com/attachment.php?attachmentid=5579&stc=1 W9.3.8 Let $S$ be the region of the xy-plane bounded above by the curve $x^{3} y = 64$ below by the line $y = 1$, on the left by the line $x = 2$, and on the right by the line $x = 4$. Find the volume of the solid obtained by...
  3. Titan97

    Volume strength of H2O2 using iodometric titration

    Homework Statement To a 25ml H2O2 solution, excess acidified solution of potassium iodide is added. The libereated iodine required 20ml of 0.3N sodium thiosulphate solution. Calculate the volume strength of H2O2. Homework Equations Normality = n-factor × Molarity Volume strength = Molarity ×...
  4. R

    VdP term in definition of constant volume specific heat

    Homework Statement I know that for constant volume ∂q=du and so du=Cv.dT However i don't understand how did we get to ∂q=du by neglecting the vdP term of enthalpy What I am trying to say is, is enthalpy this ∆U+P∂V+V∂P or this ∆U+P∂V? I don't understand since the definition of enthalpy is...
  5. F

    Volume of a Solid- 3D Calculus

    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 =...
  6. G

    MHB Evaluate this triple integral for calculating volume

    I'm tring to find this volume using a triple integral in the form $dy$ $dx$ $dz$ However I think I'm evaluating the wrong integral because the result is 1 when the volume should be 1/6... Can someone help me find out what I'm doing wrong? The set is $$V=\{(x,y,z)\in \mathbb{R^3}: x+y+2z...
  7. M

    Reaction Kinetics, batch reactor varying volume

    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...
  8. K

    Volume of Right Circular Cone: How to Calculate Using Integration

    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?
  9. T

    I Finding the volume under the curve of a rotated function

    why can't it be like this?
  10. J

    Change of volume in pure torsion

    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
  11. M

    Heat capacity at constant volume and internal energy

    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...
  12. physea

    I Does buoyancy depend on shape and volume?

    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...
  13. maxhersch

    SigFigs in Volume and Uncertainty?

    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...
  14. S

    Volume flow rate variation of a free air jet

    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...
  15. TheSodesa

    A sphere with a hole through it (a triple integral).

    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...
  16. H

    Rotational period for constant mass but different volume

    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...
  17. TheSodesa

    The volume of water gathered by a tilted paraboloid antenna

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  18. N

    MHB Maximizing volume of cone inscribed within cone

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  19. A

    I Volume of light cones of two events

    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...
  20. S

    I Volume of velocity-space in Maxwell-Boltzmann distribution

    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...
  21. Einstein's Cat

    B Volume Hypersphere: 4D Sphere Equation

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

    Volume of a solid bounded by a paraboloid and the x-y plane

    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...
  23. P

    Calculating volume between two paraboloids

    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...
  24. J

    The Pressure Distribution in a Narrowing Tube with Increasing Fluid Velocity

    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...
  25. C

    How many 0.3 micron particles in 0.1L volume of room air?

    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...
  26. Kuzon

    What's wrong with my math?[Thermal volume expansion]

    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
  27. W

    Volume of a Pond (Triple Integral)

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  28. E

    B What Methods Calculate the Volume of a Solid Revolved Around Non-Standard Axes?

    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 =...
  29. K

    Find the Mistake in Calculating Volume by Integration

    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?
  30. R

    Resistance between 2 points in infinite 3-D gas volume

    Hi Back in 2011 here https://www.physicsforums.com/threads/resistance-between-two-points-in-an-infinite-volume-of-resistive-gas.513388/ the question of the resistance between two points in an infinite volume of resistive gas was raised but petered out without a solution. The solution could be...
  31. M

    How Do Volume Expansions Differ in Liquids and Gases Due to Temperature Change?

    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)...
  32. Berenices

    I How to Define a Shape Based on Variables

    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...
  33. x2017

    How Do You Calculate the Volume of a Floating Object?

    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...
  34. M

    Find Heat Energy Needed to Expand Gas to Triple Volume

    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...
  35. G

    Potential divider to adjust volume and sensors

    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
  36. F

    Calculating Specific Volume from a Question: Tips & Tricks

    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
  37. C

    Solving for mass of a solute given ppm and volume?

    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...
  38. R

    Power consumption for maintaining Temp in a control volume

    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...
  39. A

    Use of Entropy for a Control Volume in Energy Balance

    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...
  40. evinda

    MHB Finding the Volume of a Parallepiped: Exploring Strategies

    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...
  41. P

    Thermodynamic definition of volume

    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...
  42. M

    Fill Balloons Homework: Max # People for Bday Party Balloon

    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...
  43. R

    Relationship of bulk modulus and fractional volume change

    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?
  44. W

    Calculating Volume: Integrating Pressure & Area

    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
  45. O

    Volume of Revolution By Shell Method.

    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...
  46. D

    Thermochem, thermodynamics, diatomic gas at constant volume

    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...
  47. P

    Find largest possible volume (Extreme Value)

    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...
  48. grandpa2390

    What is the volume of the gas after adiabatic compression

    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...
  49. Titan97

    Thermodynamics problem involving piston and spring

    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...
  50. D

    How Do You Calculate the Volume of a Solid Rotated Around y=1?

    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...
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