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Determine initial and final temperatures, adiabatic expansion?

  1. Feb 4, 2013 #1
    1. The problem statement, all variables and given/known data

    A 3.25 mol sample of an ideal diatomic gas expands adiabatically from a volume of 0.1050 m^3 to 0.762 m^3. Initially the pressure was 1.00 atm

    Determine the initial and final temperatures

    2. Relevant equations

    PVγ= nRT

    3. The attempt at a solution

    To get the initial temperature, I used the above equation

    *note: converted atm to N/m^2

    T = PVγ/nR = (1.013 *10^5 N/m^2)((0.1050 m^3)^1.4)/ (3.25 mol * 8.314 J/mol*K)

    T = 159.8 K

    Unfortunately that isn't the correct answer and the correct answer is actually 394 K. I'm pretty sure I'm going through the steps correctly. But no matter how I put the above into the calculator, I keep getting the wrong answer.

    All help is appreciated! :)
     
  2. jcsd
  3. Feb 5, 2013 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The equation marked with red is wrong.
    PV=nRT for an ideal gas. And pVγ= const during an adiabatic process.

    ehild
     
  4. Feb 5, 2013 #3
    You should first use P1V1γ = P2V2γ to evaluate for final pressure of the gas.

    And , PVγ= nRT is wrong ! Its PVγ=constant. Also it will be correct to write PV=nRT....

    Hint : What is γ for diatomic gas ?
     
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