What is Density: Definition and 1000 Discussions

The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:




ρ
=


m
V




{\displaystyle \rho ={\frac {m}{V}}}
where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight.
For a pure substance the density has the same numerical value as its mass concentration.
Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure.
To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one relative to water means that the substance floats in water.
The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid. This causes it to rise relative to more dense unheated material.
The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass.

View More On Wikipedia.org
  1. D

    Density of star from hydrostatic equilibrium and pressure

    Homework Statement Assume that the pressure p in a star with spherical symmetry is related to the density \rho by the (distinctly unrealistic) equation of state p= \tfrac12 k\rho^2, where k is a constant. Use the fluid equilibrium equation obtained in Problem 23 to find a relation between \rho...
  2. F

    Volumentric or surface charge density

    Homework Statement It is known that the potencial is given as V = 80 ρ0.6 volts. Assuming free space conditions, find a) E, b) the volume charge density at ρ=0.5 m and c) the total charge lying withing the closed surface ρ=0.6, 0<z<1 Homework Equations E[/B]=-∇VThe Attempt at a Solution (this...
  3. F

    Estimating Atmospheric Params w/ Autocorrelation & Spectral Density Funcs.

    Homework Statement An experiment probes a coherent process and the receiver is coherent. The autocorrelation function and the spectral density function are estimated and transformaed into atmospheric parameters. See Table 1 below 1) Calculate the maximum velocity (in m/s) that may be...
  4. J

    Electric Field Energy Density: Plates of Q & A

    Homework Statement Two large non-conducting plates of surface area A=.025m^2 carry equal but opposite charges Q = 75microC. What is the energy density of the electric field between the two plates. Homework Equations I wrote the equations on my attempt. This was a multiple choice problem...
  5. W

    I Why is the density infinite at the singularity?

    I always has the impression that the density of the universe is infinite at the singularity because its just amount of stuff divided by volume and if the distance between stuff is 0 then the volume is 0. So divide by zero and you get infinity. But I have been told by others that dividing by zero...
  6. defaultusername

    What is the mass of ceramic on the wire with non-uniform coating?

    Homework Statement A metal wire is given a ceramic coating to protect it against heat. The machine that applies the coating does not do so very uniformly. The wire is in the shape of the curve The density of the ceramic on the wire is Use a line integral to calculate the mass of the...
  7. P

    1A caused by half the charge density at twice the velocity

    In the situation consisting of a steady current of 1A in an arbitrary closed path, what would the consequences be for the electric field if the drift velocity was non-uniform along the path due to non-uniform carrier density? This would be a case of a "uniform" 1 amp, but where the charge...
  8. E

    I Planck formula and density of photons

    Hello! Let's consider again a system of atoms with only two permitted energy levels E_1 and E_2 > E_1. When electrons decay from E_2 level to E_1, they generate a photon of energy E_{21} = E_2 - E_1 = h \nu. The number of photons (per unit frequency, per unit volume) emitted by such a system in...
  9. entity314

    Flux Density in Mutual Induction Solenoid with Core

    For a standard solenoid, I've found that B=μnI where μ = permeability of the core (4π×10^-7 for free space) n = number of coils I = current Firstly, is the permeability of soft iron 0.08, as I found? Primarily, however, I'm wanting to know if this still applies for a mutual induction apparatus...
  10. Karan Punjabi

    Oxygen Charge & Electron Density in Simple Carboxylic Acids

    In any simple carboxylic acid there are two oxygen atoms then i have a confusion that which oxygen has more negative charge on it or which one has the most electron density on it?
  11. Davephaelon

    I Calculating Cooper Pair Density in Niobium/YBCO

    Is it possible to calculate the average number of Cooper-pairs, existing at any given moment, per cubic centimeter of niobium (or YBCO), at their critical temperatures? I realize that Cooper pairs form and dissolve continuously, and constantly change partners, so perhaps its not easy to...
  12. 1

    I Why do we calculate the density of states using k-space?

    In statistical physics the calculation to obtain the density of states function seems to involve an integral over an eighth of a sphere in k-space. But why do we bother moving from n-space to k-space, if there's a linear relation between n and k i.e. n = (L/π)k ? Why don't we just integrate over...
  13. L

    Density matrix spin half, Pauli vector

    A nice discussion of the density operator for a qubit can be found here: http://www.vcpc.univie.ac.at/~ian/hotlist/qc/talks/bloch-sphere-rotations.pdf
  14. R

    Melt drop radius, surface tension and its density

    i am trying to figure out the relationship between diameter of a drop of liquid, its density and its shape. Can somebody explain to me the following two lines?
  15. Spinnor

    B Energy density of charged capacitor via QFT

    From the view point of quantum field theory how does one describe the electromagnetic energy density between the plates of a charged capacitor? Thanks!
  16. C

    A Relativistic conduction current density?

    Hello, I am an electrical engineer rather than a physicist, however, I am trying to understand the physics of a twin wire transmission line in terms of the charge and current density. Let's say we have a lossless, infinite length, twin wire transmission line, a step current is induced into the...
  17. U

    Is the current density a vector?

    In Newtonian physics, is the current density, usually called j, a vector? Namely, is it a polar vector in the sense of a tensor of rank 1?
  18. S

    Floating block with objects that are thrown in a liquid

    Homework Statement I'm confused about the following kind of situation. Consider a block of density ##\rho_b##, mass ##M_b## and section ##S_b## that floats on a liquid of density ##\rho_l##, in a tank of section ##\mathcal{S}##. On the block there are some objects (all equal), of density...
  19. H

    Derive energy density proportional to emitted power per unit area

    The following derives the relation that for a blackbody radiation the energy density is proportional to the energy emitted per unit area over unit time. The average energy density ##d\psi## is obtained by dividing the radiant energy ##dE## received by the surface ##dB## in 1 second by the...
  20. Arnd Obert

    I Density of states with delta function

    Hello, I'm stuck with this exercise, so I hope anyone can help me. It is to prove, that the density of states of an unknown, quantum mechanical Hamiltonian ##\mathcal{H}##, which is defined by $$\Omega(E)=\mathrm{Tr}\left[\delta(E1\!\!1-\boldsymbol{H})\right]$$ is also representable as...
  21. P

    I Does the 1 Second after the Big Bang = 1 second now?

    When I read that conditions were such and such 1 to .05 seconds after the big bang, is that duration somehow longer than 1/2 second is now (maybe because of the difference in density or like the twin paradox?)?
  22. munirah

    I How reduced density matrix obtained from the matrix.

    Can any expert help me in explaining how this example below get the reduced density matrix from the density matrix in bipartite system. $$\rho =\frac{1}{4}\begin{pmatrix} 1 & 1 & cos(\frac{\alpha}{2})-sin(\frac{\alpha}{2}) & cos(\frac{\alpha}{2})+sin(\frac{\alpha}{2}) \\ 1 & 1 &...
  23. munirah

    Reduced Density operator in matrix form

    Homework Statement I already read book of Quantum Computation and Quantum Information by Nielsen and Chuang according to reduced density operator and I already understand how to do the reduced density using Dirac notation, Ket Bra.Homework Equations [/B] My problem here I want to know the...
  24. wolram

    B Density of Black Holes: Unveiling the Universe's Secrets

    It seems by this paper that there are more black holes than expected, so what is the expected density of black holes in the nearby universe? arXiv:1606.04996 (cross-list from gr-qc) [pdf, other] Constraining modified theories of gravity with gravitational wave stochastic background Andrea...
  25. J

    Water level involving Density, mass, volume, radius

    Homework Statement A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls...
  26. S

    A solid cylinder of uniform density of 0.85 g/cm3 floats in

    Homework Statement A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring. https://s1.lite.msu.edu/res/msu/kashy/physicsLib02/32_Fluids1_Pascal_Arch/graphics/archimedes.gif Its circular surfaces are horizontal. What effect will the...
  27. S

    A small solid sphere of mass M0, of radius R0, and of unifor

    Homework Statement A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls...
  28. mertcan

    I Gravitational Lagrangian density

    Hi, in gravitational theory the action integral is: I = ∫( − g ( x))^1/2 L ( x) d 4 x, but I do not know why there is a square root -g . Could you give me the proof of this integral? I mean How is this integral constructed? What is the logic of this? Thanks in advance...
  29. Just144Ice

    Find Density Given Period of Orbit

    Homework Statement A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 2.53 hours. What is the density of the planet? Assume that the planet has a uniform density. Homework Equations T^2=(4pi^2r^3)/GM V=4/3piR^3 Density= Mass/...
  30. M

    I Density of states from 3D to 2D

    Hi, I know how to calculate density of states for both cases, but it is not clearly to me how I can go from 3D case to 2D. I have energy from infinite potential well for 3D $$E=\frac{\hbar \pi^2}{2m}(\frac{n_x^2}{l_x}+\frac{n_y^2}{l_y}+\frac{n_z^2}{l_z})$$ let make one dimension very small...
  31. R

    Mass of an annulus with variable mass density

    Hey guys, I just wanted to check if my method for solving this problem is correct. 1. Homework Statement Consider an annulus with inner radius R1 and outer radius R2. The mass density of the annulus is given by σ(r)=C/r, where C is a constant. Calculate the total mass of the annulus. Homework...
  32. E

    Calculating flux density in an air gap

    I am trying to calculate the flux density of an air gap in an electromagnet. I am following this page that calculates the flux density in a C core with an air gap. My confusion is that I am using 50Hz AC instead of DC I have control over the voltage amplitude since I would be using a variac to...
  33. E

    I Fermi sphere and density of states

    Hello! When computing the density of states of electrons in a lattice, a material with dimensions L_x, L_y, L_z can be considered. The allowed \mathbf{k} vectors will have components k_x = \displaystyle \frac{\pi}{L_x}p k_y = \displaystyle \frac{\pi}{L_y}q k_z = \displaystyle \frac{\pi}{L_z}r...
  34. Will Langas

    B Are Larger Black Holes Less Dense Than Smaller Ones?

    What has a higher density? Black Holes or Singularities? I looked online and all I saw was that they both have infinite densities.
  35. J

    I Does mass density affect load distribution on barbell?

    Had an argument with a few guys at the gym today. I told them that loading a barbell with 100 on each side instead of 2 45s and a 10 causes more pressure on your spine. This example is in reference to someone performing a low bar squat in which the bar has contact points across the entire back...
  36. W

    I Vacuum energy density after inflation

    Its said that if there are different pocket universes made by inflation then this solves the alleged fine tuning of dark energy. My question is this: can the idea of different values for the vacuum energy density in these different pockets be derived from quantum field theory or does it need...
  37. entropy1

    I Expectation value in terms of density matrix

    It says in Susskind's TM: ##\langle L \rangle = Tr \; \rho L = \sum_{a,a'}L_{a',a} \rho_{a,a'}## with ##a## the index of a basisvector, ##L## an observable and ##\rho## a density matrix. Is this correct? What about the trace in the third part of this equation?
  38. S

    B Question About Density: Lower Mass, Same Volume?

    So if a car were to somehow have its density lowered by lowering the mass, but keeping the volume the same, would the car be more damageable and breakable than it was before, or would that depend on something else other than density?
  39. T

    I How is a top gate used to change electron density?

    How is a top gate used to change electron density in 2D semi conductors? I get the principle, you are just shifting the chemical potential by some voltage so that there are more or less electrons in the specific bands. But how is it physically done? Thanks.
  40. Dr. Octavious

    I Electron number density in fusion plasma

    Hello everybody, Is there a way to calculate/predict the electron number density of a plasma? Thanks in advance
  41. L

    Traveling EM waves with fixed energy density

    Hi, I'm taking an undergrad course in Electromagnetism and Optics, and in the lecture notes it reads: "Consider the formal equation ε0D⋅E = 1 ... that must be obeyed for waves traveling in different directions as defined by the wave vector k but with a given energy density." Could anyone help me...
  42. C

    A Free energy density in liquid crystals

    Hi, For someone who's familiar with LC's: How to derive the expression for free energy density of an hybrid aligned LC cell? what should be the vector for the director? I already familiar with the cases of splay and bend cell but couldn't understand how to derive it to the case where the cell is...
  43. Guy ML

    Question about polarization density

    Homework Statement Given a sphere with radius R, centered at (0,0,0), it's dipole density given as ##P\left(\vec{r}\right)=\alpha\left(R-r\right)\hat{z}## where r is the distance from the center of the ball. I'm required to find: Bound charge density inside the sphere, bound charge density on...
  44. Parsifal1

    Does gamma equal density in Kg/m^3?

    I want to use the equation: Fr='gamma'*distance from centroid*Area but the example is showing density in N/m^3 while I only have the density in kg/m^3 Does this mean I have to multiply it by 9.81 to get the right answer? Thanks.
  45. C

    A Density of Irrational Numbers in [0;1]

    Hello, let be ##x \in \mathbb{R} - \mathbb{Q}##, do we have de density of ##\{nx - \lfloor{nx} / n \in \mathbb{N}\}## in ##[0; 1]## please? I think yes but it's just an intuition : if I take a and b in ##[0; 1]## with a < b, I have an irrationnal between them let call it c but I don't know...
  46. NatFex

    I Sum of Probability Density Function > 1?

    I have a Stats exam on Wednesday and while I thought I was quite well-versed, I've gone back over to the very basics only to find myself confused at what should be introductory. Suppose I have a continuous random variable modeled by a probability density function: $$f(x)=2x$$ Obviously the...
  47. DavideGenoa

    I Relaxed conditions for the density: Ampère's law still valid?

    The most common proof that I have found of the fact that Ampère's law is entailed by the Biot-Savart law essentially uses the fact that, if ##\boldsymbol{J}:\mathbb{R}^3\to\mathbb{R}^3##, ##\boldsymbol{J}\in C_c^2(\mathbb{R}^3)##, is a compactly supported twice continuously differentiable field...
  48. L

    Statistical physics. Density matrix

    Homework Statement A system is subject to Hamiltonian ##\hat{H}=-\gamma B_z \hat{S}_z##. Write down the density matrix.[/B]Homework Equations For canonical ensemble ##\hat{\rho}=\frac{1}{Tr(e^{-\beta \hat{H}})}e^{-\beta \hat{H}}## In general ##\rho=\sum_m |\psi_m\rangle \langle \psi_m|## The...
  49. Y

    Question: pressure inside an object submerged in water

    I'm doing a question relating to the pressure inside on object submerged in water. Here is the question: A tube, height 1.2m, is submerged vertically in the ocean where the waters density is 10^3 kg/m^3. A diver initially holds the tube vertically directly on top of the water. He then dives to...
  50. EnumaElish

    B Exploring the Density of Black Holes: Common Misconceptions Debunked

    [Mentors' note: split off from this thread] Do all black holes have the same density?
Back
Top