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Finding the volume of a cube with 1 Joule

  1. Sep 20, 2011 #1
    1. The problem statement, all variables and given/known data
    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


    2. Relevant equations

    Eth = 3NKbT = 3nRT = 3pV

    3. 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!
     
  2. jcsd
  3. Sep 21, 2011 #2
    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 ?
     
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