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Why ∆u=Cv ∆T for isochoric transformation of non-ideal gases?

  1. Apr 10, 2012 #1
    I simply report what I read:
    "For an ideal gas, but for every kind of transformation ∆u=Cv ∆T, while for every kind of material in the thermodynamic system, but only for isochoric transformation ∆u=Cv ∆T."

    Where does this second statement come from?
    Everything is clear about ideal gases, but I don't figure out how to prove the second part of this statement.
  2. jcsd
  3. Apr 10, 2012 #2
    That is how Cv is defined.

    Cv is the limit when ∆T goes to zero of ∆u/∆T. The first statement is simply a consequence of internal energy being dependant only of T for an ideal gas.
  4. Apr 10, 2012 #3
    It follows from the first principle of thermodynamics. In isochoric transformations the work (compression-expansion work) is zero so Δu=Qv.
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