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Homework Help: VdP term in definition of constant volume specific heat

  1. May 3, 2016 #1
    1. The problem statement, all variables and given/known data
    I know that for constant volume ∂q=du and so du=Cv.dT
    However i dont understand how did we get to ∂q=du by neglecting the vdP term of enthalpy
    What im trying to say is, is enthalpy this ∆U+P∂V+V∂P or this ∆U+P∂V? I dont understand since the definition of enthalpy is derived out of a constant pressure volume change
    And why snt specific heat at constant volume Cv=∆U+V∂P/dT instead of Cv=∆U/dT?

    Thank you in advance for your answers
    2. Relevant equations

    3. The attempt at a solution
    From what I see:


    For constant pressure:
    Cp=∆U+P∂V/dT assuming ∆U+P∂V is enthalpy then ∆H=Cp.∆P

    For constant volume:
    Cv=∆U+V∂P/dT but all the books say it actually is just ∆U/dT
    where did the VdP term go? if we add heat to a fixed volume won't its pressure increase and so VdP would be relevant?
  2. jcsd
  3. May 3, 2016 #2
    dW = PdV, not d(PV).
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