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Homework Help: Isothermal exapansion, work done

  1. Feb 3, 2013 #1
    1. The problem statement, all variables and given/known data
    Derive an expression for the amount of work done when one mole of an ideal gas expands isothermally at a temperature T from an initial volume V1 to a final volume V2.

    2. Relevant equations
    PV = nRT
    W = V2V1Pdv

    3. The attempt at a solution
    I'm not really sure how to go about this, I know if it's isothermal the temperature doesn't change so Volume would be inversely proportional to Pressure. But other than that i don't know what to do, to be honest i'm not really exactly what they want me to write. Any help would be much appreciated :)
  2. jcsd
  3. Feb 3, 2013 #2
    The question seems to be incomplete. It is isothermal expansion , fine. But its isothermal reversible or isothermal irreversible process , its just not mentioned.

    I ask you a question : Do you want to calculate maximum work done by the gas , or not in an isothermal process. If former , consider the process reversible , else irreversible.

    Oh , they do not concern you about external pressure. Consider your process reversible then.

    Hint :

    W = V2V1Pdv ....(i)

    PV=nRT => P=nRT/V

    Now replace this value of P in (i) and carry on your integration.
  4. Feb 3, 2013 #3
    Thanks for the Hint thats makes sense, my final answer (upon using that hint) would be W = RT * Ln(V). I think that's the answer but i'll try and confirm it with my lecturer tommorow if i can. Thanks for your help.
  5. Feb 3, 2013 #4
    No you should get W=RT*ln(V2/V1)

    See your integral again. Be careful while doing integration.
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