## 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.