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Finding specific heat capacity of a non-monatomic (ideal gas)

  1. Nov 12, 2013 #1
    1. The problem statement, all variables and given/known data

    Suppose that 31.4 J of heat is added to an ideal gas. The gas expands at a constant
    pressure of 1.40x104 Pa while changing its volume from 3.00x104 to 8.00x104 m3.
    The gas is not monatomic, so the relation CP = 5/2R does not apply. (a) Determine the
    change in the internal energy of the gas. (b) Calculate its molar specic heat capacity
    CP .

    2. Relevant equations



    3. The attempt at a solution

    I have completed part a) using the knowledge that it is an isobaric process, but i'm a bit unsure of my answer for b)

    My text book says that for a diatomic ideal gas, Cp is given by 7/2 R, but the question only says the gas is not monatomic.

    Is there a piece of info i'm missing?

    Thanks!
     
  2. jcsd
  3. Nov 12, 2013 #2

    CAF123

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    Gold Member

    Because U is a state variable, you can define a path between the initial and final states of the gas where V is a constant. This will allow you to find cv, from which you can extract cp.
     
  4. Nov 12, 2013 #3
    Just apply the constant pressure version of the first law: ΔU=Q-PΔV. Also, since ΔH=ΔU+Δ(PV), which for this constant pressure process becomes ΔH=ΔU+PΔV. So, for this process ΔH=Q. For an ideal gas, ΔH=CpΔT and ΔU=CvΔT. So,
    ΔH/ΔU=Cp/Cv=(Q-PΔV)/Q. You also know that Cp-Cv for an ideal gas is equal to R. This should give you enough information to determine Cp.
     
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