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Expansion of a gas at constant temperature and pressure

  1. May 3, 2012 #1
    1. The problem statement, all variables and given/known data

    A gas expands in volume from 26.7mL to 89.3mL at constant temperature. Calculate the work done (in joule) if the gas expands:
    i) against a vacuum
    ii) against constant pressure of 1.5atm
    iii) against a constant pressure of 2.8


    2. Relevant equations

    w= -PdV

    gas expands at constant temperature= isothemic expansion

    3. The attempt at a solution

    i) I'm not sure about this part

    ii) 1atm= 1.013x10^5 Pa

    P= 1.5x 1.013x10^5 = 151950 Pa

    I converted ml to m^3 (am i supposed to do this?)

    26.7/ 1x10^6 = 2.67x10^-5 m^3

    8.93/ 1x10^6 = 8.93x10^-5 m^3

    w= -PdV

    w= - (151950)x (8.93x10^-5 -2.67x10^-5)

    w= -9.512 J

    iii) I did the same working for this part as above

    P= 2.8 x 1.013x10^5

    P= 283640 Pa

    w= - (283640) x (8.93x10^-5 -2.67x10^-5)

    w= -17.756 J

    am I doing this correct? or do I use the equation ln V2/V1 P ?
     
  2. jcsd
  3. May 5, 2012 #2
    i) That's free expansion; It's as if the gas is 'doing work' by pushing a massless piston in space since there's no opposing force as the gas expands.

    ii & iii) It's isothermal expansion, so P varies as the volume changes. The equation W = -P ∆V doesn't work anymore and W = -∫ P dv, is used instead.

    Also, yeah, it's better to convert ml to cubic meters since it's simpler to keep everything in the MKS system of units.
     
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