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Homework Help: Finding the pressure and temperature of a compressed monatomic gas

  1. Aug 24, 2010 #1
    1. The problem statement, all variables and given/known data

    A monatomic ideal gas initially has a volume of 3 m^3, a temperature of 300 K and
    is at a pressure of 1x 10^5 Pa. It is compressed adiabatically and quasi-statically to a
    volume of 2 m^3. Calculate its final pressure and temperature.

    2. Relevant equations

    Po(Vo ^gamma)= P1(V1^gamma)
    PV= NKbT

    3. The attempt at a solution

    degrees of freedom (nd)= 3
    gamma = nd+2/ nd = 5/3
    Vo = 3m^3 ; V1= 2m^3
    P0 = 1x10^5Pa ; P1 = ?

    The new pressure ; P1 = 1.97 x 10^5 Pa

    Re-arrange to get T= P1V1 / N Kb
    N = V0 / 22.47 x 6.02 x10^23 (avogadro's number) = 8.036 x10 ^25

    So T = 355.23K

    I understand the method, but I do not understand where the value of 22.47 comes from. But i think that V0/22.47 is to find the number of moles. Help please?
  2. jcsd
  3. Aug 25, 2010 #2
    22.4 is the volume (in liters) of one mole of an ideal gas at STP. So yes, it converts from volume to moles.
  4. Aug 25, 2010 #3
    Ar ok, thank you very much. I'll keep that figure in mind in the future. :)
  5. Aug 27, 2010 #4


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    Gold Member

    It converts from moles to liters at STP. Unfortunately the problem specifies the initial temperature is 300K so the factor is more like 24.9 L/mol.

    Special bonus item - standards bodies do not agree on what STP conditions are. But the informal standard is 0C/1 atm.
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