Question

In deep space, the dumber density of atoms is 10^6 atoms/m^3 and the temperature is 2.7K. What volume in cubic meters is occupied by 1.5 mol of gas? If this volume is a cube, what is the length of one of its edges?

Answer 1

Answer on Question #75790, Physics / Mechanics — Relativity

Question In deep space, the dumber density of atoms is $10^{6}$ atoms/m^{3} and the temperature is 2.7K. What volume in cubic meters is occupied by 1.5 mol of gas? If this volume is a cube, what is the length of one of its edges?

Solution We will use following relation for ideal gas:

$p=nkT$

from where we can find the pressure:

$p=10^{6}\cdot 1.38\cdot 10^{-23}\cdot 2.7\approx 3.7\cdot 10^{-17}\,Pa$

Next we use

$pV=\nu RT$

from were we can find volume of 1.5 mole:

$V=\frac{\nu RT}{p}=\frac{1.5\cdot 8.31\cdot 2.7}{3.7\cdot 10^{-17}}\approx 9.1\cdot 10^{17}\,m^{3}$

So that would cube with edge:

$\sqrt[3]{V}\approx 969\,km$