Finding the volume of a cube with 1 Joule

[pdonovan]

Homework Statement

Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not ). The number density is about and the temperature is about 3 K.

What is the edge length L of an LxLxL cube of gas with 1.0 J of thermal energy?

I found:
P = 4.14x10^-17Pa
Vrms = 273m/s

Homework Equations

Eth = 3NKbT = 3nRT = 3pV

The Attempt at a Solution

Eth = 1J

Eth = 3pV = 3(4.14x10^-17)V
--> V = 8.05x10¹⁵

Is this the correct answer or is my math wrong somewhere? Thank you for any input!

 

[Spinnor]

The average kinetic energy of an atom in a gas at temperature T is,

E = 3/2kT

k = 1.38E-23 J/K
T = 3 degrees K

E = 6.21E-23 J

If the density of atoms was 1/m^3 then X*6.21E-23 J = 1 J ?

X=1.61E22 atoms in 1.61E22m^3 of space. The cube root of 1.61E22m^3 = 2.52E7 m = L ?