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:



{\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.

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  1. Ranku

    I Flat universe density parameter

    For a flat universe, density parameter Ωuniverse=1. How does negative signage of a constituent density parameter, such as that of curvature index Ωk, which can be 0,1,-1 affect the signage of Ωuniverse? If Ωk were to be converted to its energy density, which is much less than the energy density...
  2. B

    How can I calculate the Density and Volume of a mechanical mixture (atoms)?

    Is it correct that: density = [ 0.09 * (density of NaCl) ] + [0.91 * (density of water) ] volume = [ (volume of water) + ( { (volume of NaCl) / 48} * 9) ] Thank you so much for any advice.
  3. Vanadium 50

    I Black Holes in Curved Spacetime

    We've been talking in another thread about supermassive black holes. That has me thinking about really, really big BH's - so large that the spacetime curvature and evolution of the universe matters. Let's start by defining the density of a black hole as its mass divided by the volume enclosed...
  4. T

    Confusion on product rule for mass of differential volume element

    Good evening, I'm running into some trouble with this problem, and I have a hint as to why, but I'm not completely sure. Please see the steps below for context. I've been able to set up the proper equation representing the density as a function of distance from the center which looks like this...
  5. W

    Density calculation sometimes can be confusing

    Ok, let's compare two cubes of lead. First lead cube weigh 6078 grams and its area is 3376 cm. The second lead cube is smaller and lighter at 5216 grams and 2713 cm area. The density of the first lead cube which is the bigger and heavier lead (by dividing its weight with the area) is 1.800 g/cm2...
  6. M

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    I am not sure if my report is complex enough as it should be at the undergraduate level preferably based on the requirements for it and it feels like it's all over the place as of now.
  7. J

    Calculate the bouyancy of two spheres joined by a rope submerged in seawater

    m * g = mAl * g V * ρ * g = VAl * ρAl * g V * ρ * g = V * ρAl * g ρ = ρAl this does not work at all, because the upper ball must have a density smaller than that of seawater 1200kg/m3 or not?
  8. E

    Density of Flow Along a Tube Under the Action of Advancing Piston

    I'm trying to figure out how describe the mass of air between the piston face and the und of the tube ( position ##o##) in the acompanying diagram. At ##t = 0##, the mass of air in the tube is ##M_o##, and the system is static with tube length ##l##. The ##x## coordinate describes how far...
  9. C

    Deriving density formulae from first principles

    Can someone please help derive the relations below from first principles? Also does someone please know what happens when ##ρ_{object} = p_{fluid}##? Many thanks!
  10. I

    Integrate disk mass density

    I want to find the cumulative mass m(r) of a mass disk. I have the mass density in terms of r, it is an exponential function: ρ(r)=ρ0*e^(-r/h) A double integral in polar coordinates should do, but im not sure about the solution I get.
  11. S

    I How is Lorenz-Lorentz relationship possible?

    Its form is: (n2-1)/(n2+2)=(4π/3)Nam There is one simple problem with it. Rearrange the left side and you get: (n2+2-3)/(n2+2)=(4π/3)Nam 1-(3/(n2+2))=(4π/3)Nam As you see, the left side cannot reach unity for arbitrarily large n2. But there is no reason why N cannot be arbitrarily large! How...
  12. ergospherical

    Density of a patch of an accretion disk

    In the frame of the patch ##-(1/\rho) \nabla p = - \nabla \phi##, and putting ##\nabla p = (\partial p/\partial \rho) \nabla \rho = c_s^2 \nabla \rho## and taking the ##z## component gives\begin{align*} -\frac{c_s^2}{\rho} \frac{\partial \rho}{\partial z} = -c_s^2...
  13. MatinSAR

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  14. E

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    The starting point is the identity $$\left(\frac{\partial u}{\partial T}\right)_n = T\left(\frac{\partial s}{\partial T}\right)_n.$$ I then try to proceed as follows: Integrating both with respect to ##T## after dividing through by ##T##, we find $$ \int_0^T \left(\frac{\partial s}{\partial...
  15. chasrob

    Inflation era energy density

    I need the theoretical energy density of inflation for my story. I seem to recall it as an enormous 1095 ergs per cubic centimeter.
  16. Mohammad-gl

    A Can I calculate partial density of states using tight binding?

    I am studying a 2D material using tight binding. I calculated density of states using this method. Can I also calculate partial density of states using tight binding?
  17. richard_andy

    A Relation between the density matrix and the annihilation operator

    This question is related to equation (1),(3), and (4) in the [paper][1] [1]: https://arxiv.org/abs/2002.12252
  18. Ranku

    I Dark energy density proportion

    Is there a way to independently determine the proportion of dark energy density to total energy density of the universe apart from using 1 -(Ωmatter+Ωdark matter )?
  19. rokiboxofficial Ref

    Surface density of the charges induced on the bases of the cylinder

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  20. R

    Phonon Density of States (PDOS) at Gamma Point

    Hello everyone! I'm trying to replicate phonon density of states (PHDOS) diagrams for some solids using Quantum Espresso. The usual way I do it is the following one: scf calculation at minima (pw.x) Calculation of dynamical matrix in reciprocal space with nq=1 or 2 (ph.x) Calculation of...
  21. Addez123

    Solving the Density of States: Understanding dn/dE

    $$n = \sqrt{n_x^2 + n_y^2 +n_z^2}$$ $$E = \frac{n^2 \pi^2 \hbar^2}{2mL^2}$$ $$n = \sqrt{ \frac{2mL^2E}{\pi^2 \hbar^2} }$$ This is all given by the textbook. It's even as friendly as to say $$\text{differential number of states in dE} = \frac{1}{8}4 \pi n^2 dn$$ $$D(E) = \frac{...
  22. Ranku

    I Density parameter and curvature index

    For Ω=1, κ=0. Does the value of κ simply follow from the value of Ω, or can its value have an independent existence? So if Ω>1, does κ have to be 1?
  23. M

    I Derivation of two-electron density operator

    Hello, I am going over the derivation for two-electron density. I am having a hard time understanding how the second term in 2.11a seen below is derived. I know this term must eliminate the i=j products but can't seem to understand how. Thanks for the help.
  24. R

    Energy Density with a Dielectric

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  25. L

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  26. F

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  27. P

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  28. patric44

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  29. C

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  30. C

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    For part a: I know that linear charge density is the amount of charge per unit length, and we are given the volume charge density. Since we are given the volume, we can obtain the length by multiplying the volume by the cross sectional area, so C/m^3 * m^2 = C/m. The cross sectional area of a...
  31. S

    Calculate the density of composite materials

    Hello Please help me. I'm not a chemistry student and I don't have a chemistry-related course, so please explain in a very simple way. Thank you. I have a composite composition that I only have the weight percentage of atoms and I need to calculate the density so that I can check the properties...
  32. V

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    When arriving at the standard model of cosmology, i.e. the exapnding universe, we assume based on experirmental data that the cosmos is homogenous on large enough scales. But when we go back in time, when the galaxies are beginning to form, we note that because of the growth of density...
  33. DANIELWR1998

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  34. maryelin

    How to get the density equation using the Reidel Equation for vapor liquids?

    I need to know how to get the density equation using the Reidel Equation for vapor liquids... how is the calculations to get
  35. P

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  36. yucheng

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  37. yucheng

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    From Rand Lectures on Light, we have, in the interaction picture, the equation of motion of the reduced density matrix: $$i \hbar \rho \dot_A (t) = Tr_B[V(t), \rho_{AB}(t)] = \Sigma_b \langle \phi_b | V \rho_{AB} -\rho_{AB} V | \phi_b \rangle = \Sigma_b \phi_b | \langle V \rho_{AB} | \phi_b...
  38. G

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  39. V

    Why does less dense air rise and more dense air come down?

    My answer given below seems incomplete. Since warm air causes the air to expand in volume, so its density becomes less as compared to the colder air at the top of the room. After this, I generally find all books saying the less dense air rises and more dense air from top comes down and...
  40. S

    I Deriving expression for resistance in terms of current density

    Is there a way to obtain equation 9.42 (I is current, j is current density, and sigma is conductivity) in the following image (from Modern Electrodynamics by Andrew Zangwill, the part on electromotive force) besides using V=IR and substituting the line integral of j/conductivity for V? The...
  41. Shreya

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    I developed three arguments to answer this question. Argument no 2 seems to be wrong, but I cant figure out why. I know one/more of my arguments are flawed. Please be kind to help me figure this out. Argument 1) Since they have same charge on them, the ##E## between them must be same. The one...
  42. M

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  43. cwill53

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  44. chwala

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  45. W

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  46. tbn032

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  47. Barbequeman

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  48. O

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