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Heat capacities of ideal gases

  1. Oct 14, 2012 #1
    1. The problem statement, all variables and given/known data

    A cylinder contains 0.2mol of Helium at 30 degrees C and is heated different ways.
    How much heat is needed to raise the temperature to 70C while keeping thevolume constant?

    2. Relevant equations

    dQ=dU+dT
    nCpdT=nCvdT+nRdT



    3. The attempt at a solution

    What I am confused about is whether to use the nCpdT (heat added) or nCvdT (change in internal energy). If it is a constant volume process, wouldnt that mean dQ=dU therefore nCpdT=nCvdT?

    Obviously that is not the case as the moles (0.2) are constant as is the change in temperature (70-30=40C or 40K). As as result Cp=Cv which should be untrue for a monatomic gas.

    What is the cause for this discrepancy and how can I determine which equation to use?

    Thanks
     
  2. jcsd
  3. Oct 17, 2012 #2

    rude man

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    Homework Helper
    Gold Member

    The problem doesn't state to assume an ideal gas. But if we do:

    You mentioned dU = dQ for any isochoric process, which is correct. So use that relation.

    Why do you invoke Cp at all? It's obviously not an isobaric process. And Cp is never equal to Cv - monatomic gas or not.
     
  4. Oct 17, 2012 #3
    It says the volume is kept constant - isochoric process it is.
    nevermind this part I for some reason read at first you were heating hydrogen and I was thinking, hang on, hydrogen is a 2atom gas - but yes, "He" is a monatomic gas.

    In case of ideal gases there is a rule:
    c = c' / ρ0
    c - amount of heat to heat up 1kg of gas by 1K
    c' - amount of heat to heat up 1 m³ of gas by 1K
    ρ0 - density of the gas in case of normal conditions where pressure is equal to 760mmHg(101325 Pa I think it was) and temperature = 273,15K

    also:
    c= C / μ
    C - amount of heat to heat up 1 mol of gas by 1K
    μ - the unit is 1kg/kmol - shows you how much is the mass of the gas in your given volume.

    To find the amount of heat, assuming there will be no loss of heat, you need to apply the formula
    Q = nCΔT or Q = mcΔT or Q = Vc'ΔT
    n - the amount of mols of your gas
    m - the mass of your gas
    V - the volume of your gas

    Cv in case of a monatomic gas is roughly 12.56 kJ/kmol
     
    Last edited: Oct 17, 2012
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