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Homework Help: Adiabatic process in a monatomic ideal gas

  1. Sep 5, 2010 #1
    1. The problem statement, all variables and given/known data
    In a quasistaic adiabatic process in a monatomic ideal gas PV^5/3 = constant [DO
    NOT PROVE]. A monatomic ideal gas initially has a pressure of P0 and a volume of
    V0. It undergoes a quasistatic adiabatic compression to half its initial volume. Show
    that the work done on the gas is

    W = 3/2 P0V0 ( 2^(2/3) - 1)

    2. Relevant equations

    dU= dQ + dW
    dW= -p dV
    V1= V0/2

    3. The attempt at a solution
    dU= dW as adiabatic procees means dQ=0

    dU= 3/2 NKbT = -p dV

    And I don't know what to do next.

    3/2 NKbT= P0Vo[1-V1/V0]
  2. jcsd
  3. Sep 5, 2010 #2


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    Homework Helper
    Gold Member

    You have given the definition of the work done on the gas:

    [tex]W=\int P dV[/tex]

    HINT: Now if you were given P as a function of V you could calculate the integral explicitly.
  4. Sep 5, 2010 #3
    I'm sorry, I don't quite understand what I should do.
  5. Sep 5, 2010 #4

    Andrew Mason

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    Science Advisor
    Homework Helper

    Use [itex]PV^{5/3}=\text{constant}[/itex] to find the final P. Then find the temperature from the Pf and Vf. Use that to determine the change in internal energy, which as you have stated must equal the work done by the gas.

  6. Sep 5, 2010 #5
    Ok, thank you!
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