What is average density – quora gasbuddy app


Say e.g., that you have a one kg (1 000 g) mass in one cubic decimeter, made up of 1 000 cm [math]^3[/math] cubes of varying mass — some > 1 g, some < 1 g, and some = 1 g mass. The average density of the box = 1 000 (g) / 1 000 (cm [math]^3[/math]) = 1 g/cm [math]^3[/math], just as if it was a homogeneous block of a substance of that density.

The density, or more precisely, the volumetric mass density, 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:

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.

One extreme “average density” is that of the whole Universe — if we accept published scientific estimates [math]^{[1]}[/math] of total mass (10 [math]^{53}[/math]kg) and volume (4×10 [math]^{80}[/math]m [math]^3[/math]), the term “average density” takes on a whole new meaning:

The theoretical “unified atomic mass” (unit u (or Da), roughly the mass of one proton) is 1.6605×10 [math]^{-27}[/math]kg . Calculating a rough total number of protons in the Universe, 10 [math]^{53}[/math]kg/1.6605×10 [math]^{-27}[/math]kg [math]≈[/math] 6×10 [math]^{79}[/math], “pretty close” to the often cited value 10 [math]^{80}[/math] (one estimate of N [math]_{Edd}[/math], Eddington’s number). [math]^{[2]}[/math]

Disclaimer: My results (based on Wikipedia inputs) deviate considerably from those published in Wikipedia … One of us is wrong, but I don’t know what kind of math the Wikipedia scientists used (I notice that the author figured the Universe volume based on a Universe radius ≈ 46.5 Gly , which would explain some of the density discrepancies (e.g., it is clear that the NASA/WMAP cosmologists (astro-physicists?) have used a Universe radius ≈ 13.8 Gly) [math]^{[4]}[/math] — I have double-checked my own numbers, but cannot see my error(s) … If someone could find them — and correct me — would be Great!

[3] I find it interesting that the “critical” Universe density — which in theory tells us if the Universe “curvature” is negative, “flat” ( i.e., critical density = actual density), or positive — can be calculated based only on the “Hubble parameter,” current “best value” H [math]_0[/math]= 70 km/s/Mpc and Newton’s constant!

The formula is ρ [math]_{Crit}[/math] = 3 H [math]_0^2[/math]/(8 πG), and if we plug in the numbers we get ρ [math]_{Crit}[/math] ≈ 9.2042×10 [math]^{-27}[/math] kg/m [math]^3[/math] — so in this crude calculation, the estimated Universe density is about 37 times lower than the critical density, which would mean that the Universe curvature is negative (whatever that might mean to the price of rice in China) — something is off here …

WMAP determined that the universe is flat, from which it follows that the mean energy density in the universe is equal to the critical density (within a 0.5% margin of error). This is equivalent to a mass density of 9.9×10 [math]^{-27}[/math] kg/m [math]^3[/math], which is equivalent to only 5.9 protons per cubic meter.