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Specific heat at constant volume

  1. Sep 18, 2012 #1
    [tex] C_{V} = \frac{∂U}{∂T} [/tex]

    This is the specific heat at constant volume so I assume it can only be used at constant volume. However, my textbook uses this to derive the following equation for reversible adiabatic expansion:

    [tex] P_{1}V_{1}^{γ} = P_{2}V_{2}^{γ} [/tex]

    Why are we allowed to use [itex]C_{V}[/itex] when it only works in isovolumetric processes?

  2. jcsd
  3. Sep 18, 2012 #2
    How is Cv used to derive the equation for adiabatic transformation?
    Can you show it here?
  4. Sep 18, 2012 #3
  5. Sep 19, 2012 #4
    The change in internal energy has the same expression for any process between two states. For ideal gas is
    [tex]\Delta U = nC_v\Delta T[/tex]
    The amount of heat is dependent on the type of process. It is [tex]Q = nC_v\Delta T[/tex]
    only for constant volume process.
  6. Sep 19, 2012 #5
    Superb! Thanks!

  7. Sep 19, 2012 #6
    For an ideal gas, the internal energy is a function only of temperature, such that dU = CvdT always. For an adiabatic expansion, dQ = 0, so that

    dU = CvdT = -pdV
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