1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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 ?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook