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Adiabatic, Isothermal and Isochoric Processes

  1. Jun 5, 2014 #1
    1. The problem statement, all variables and given/known data

    An ideal gas with Cv = (5/2)R, and Υ = 1.40 undergoes an adiabatic expansion until it has a pressure of 1.0*10^5 Pa and a volume of 2.0m^3. It then undergoes an isothermal contraction of T=300K until it has a volume of 1.0m^3, and then undergoes an isochoric (constant volume) heating until it reaches its original pressure and temperature.

    What is Q during the isochoric heating?

    2. Relevant equations

    These are the previous questions that I have already answered and know are correct.

    What is the pressure in the gas before the start of the adiabatic expansion?
    2.6*10^5 Pa

    How much work is done by the gas during the isothermal contraction?
    -1.4*10^5 J

    3. The attempt at a solution

    At the start of the isothermal contraction (number of moles)-
    PV = nRT
    n = PV/RT
    n = (1.0*10^5)(2.0)/(8.314)(300)
    n = 80.19

    At the start of the adiabatic expansion (finding final temp for isochoric heating)–
    PV = nRT
    T = PV/nR
    T = (2.6*10^5)(1.0)/(8.314)(80.19)
    T = 389.98

    For the isochoric heating –

    Q = nCvΔT
    =(80.19)(5/2)(8.314)(389.98 – 300)
    = 1.5*10^5 J

    The correct answer is 1.6 * 10^5 J, so I am not really sure where I have gone wrong!
     
  2. jcsd
  3. Jun 5, 2014 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You rounded off the initial pressure too early. Keep two more digits.

    ehild
     
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