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Thermal physics - how are Cp and Cv used?

  1. Jan 8, 2014 #1
    Afternoon all.

    I've have the following equations:

    Cp - Cv = nR = Nkb

    Cv = nRf / 2

    Cp = nR(2+f) / 2

    CvlnT = -nRlnV + const

    where f is degrees of freedom

    Do the Cp and Cv just stand for pressure and volume (where both are constant), so for example can the first equation only be used for a system that is isobaric and isochoric?
     
  2. jcsd
  3. Jan 8, 2014 #2

    Simon Bridge

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    The subscript refers to the state variable held constant in order to measure the corresponding heat capacity.

    The first equation gives the relation between the heat capacities - it would be used, for instance, to infer one from knowledge of the other.
    http://en.wikipedia.org/wiki/Heat_capacity

    There's no special reason that a isobaric or isochoric process must be happening for the different capacities to be used. Heat capacities are a material property.
    i.e. in an Adiabatic process, both (in ratio) are used yet pressure and volume both change.
     
  4. Jan 8, 2014 #3
    Ah ok, now the C makes sense.

    So I might be given a value for Cp and what that means is: # moles of this gas was raised by # Kelvin/°C with the pressure kept constant?
     
  5. Jan 8, 2014 #4

    Simon Bridge

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    Yah.
    The Cp, say, would be given for the entire sample though, and it does not have to be a gas.
    It literally means that if you raised the temperature of the sample by 1 unit while keeping the pressure a constant, and without changing phase, then you used 1 unit of energy.

    What counts as 1 unit depends on what units Cp was quoted in.
    In SI units, that would be K and J.
     
  6. Jan 8, 2014 #5
    cool thanks simon
     
  7. Jan 8, 2014 #6
    A mathematically precise definition of the molar heat capacities which never fails is

    Cp=∂H(T,P)/∂T

    and

    Cv=∂U(T,P)/∂T

    where H is the enthalpy and U is the internal energy.

    Chet
     
    Last edited: Jan 8, 2014
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