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Homework Help: Total Internal Energy of an Ideal Gas

  1. May 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Argon is stored in a container of volume 2L and a pressure of 5 atmospheres. The amount of gas present is 0.2 moles. Find:

    (i) The absolute temperature of the gas
    (ii) The number of atoms of gas in the container
    (iii) The total mass of the gas
    (iv) The total internal energy of the gas.

    You may assume argon behaves as an ideal gas, the atomic mass of argon is 40 g/mol.

    2. Relevant equations

    PV = nRT
    dU = Uf – Ui = Q – W (First Law of Thermodynamics)

    3. The attempt at a solution

    (i) I used PV = nRT, made all the relevant conversions and got 364.4 K. Think it's right.
    (ii) I multiplied 0.2 (number of moles) by Avegadro's constant (6.02x10^23) and got 1.204x10^23 atoms. Think it's right.
    (iii) I'm not sure if this is right... To find the total mass of the gas, knowing that the atomic mass is 40g/mol, I just multiplied 40 by 0.2 and got 8g?
    (iv) I haven't a clue. :( The only equation I can find for total internal energy is the First Law of Thermodynamics above, but as far as I know, I don't have any of those things or know how to find them.

    Thanks very much for any help!
  2. jcsd
  3. May 7, 2012 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    I get a different number. P = 5 x 101,325 Pa; V = .002 m^3; n = .2 mol; R = 8.314 J/K mol
    Right. This is correct because Argon is a noble gas so it is a monatomic gas.
    Use U = nCvT

  4. May 7, 2012 #3
    Aw, brilliant, I think I have it, thanks!

    (apologies about the temperature calculation, the question is actually 3 atmospheres and that's what I used, I accidentally typed 5 on here, sorry!)

    U = n Cv T

    where n = 0.2
    T = 364.4 K
    and Cv = 3/2 R = 12.47

    when I put them all into the equation I get 911 J.

    Thanks a million for your help, very much appreciated :)
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