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Homework Help: Compressing ideal gas isothermally, calc work

  1. Apr 15, 2010 #1
    1. The problem statement, all variables and given/known data

    10 moles of an ideal gas are compressed isothermally and reversibly from 1 to 10 atmospheres at 300K. Determine the work done ON the gas.


    2. Relevant equations

    dw=-PdV
    PV=nRT

    3. The attempt at a solution

    dT=0
    T=300K
    dP=10atm

    calc dV from ideal gas law = 2.27e10 m^3

    so now we have dV for work eqn, but P is not constant?

    Thanks.
     
    Last edited: Apr 15, 2010
  2. jcsd
  3. Apr 15, 2010 #2
    As much as I don't like thermodynamics, it doesn't seem very complicated.
    Start with claperyon equation nr. 1:
    p1V1=nRT
    which allows you to calculate the first volume.
    Equation nr.2:
    p2V2=nRT
    allows you to calculate 2nd volume. Hence you've got your integrating limits.
    Now, I wish I knew how to use TeX in here :/.
    Anyway,
    [tex]
    W=\int\limits_{v_1}^{v_2} pdV [/tex]
    As you mentioned, p is not constant, but you can, again, calculate it easily from clapeyron's equation:
    pV=nRT. And then substitute p under integral with what you've got, integrate. Should get natural logarithm.
     
    Last edited: Apr 15, 2010
  4. Apr 15, 2010 #3
    Thank you, irycio!
     
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