Thermal physics - how are Cp and Cv used?

[Flucky]

Afternoon all.

I've have the following equations:

C_p - C_v = nR = Nk_b

C_v = nRf / 2

C_p = nR(2+f) / 2

C_vlnT = -nRlnV + const

where f is degrees of freedom

Do the C_p and C_v 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?

 

[Simon Bridge]

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.

 

[Flucky]

Ah ok, now the C makes sense.

So I might be given a value for C_p and what that means is: # moles of this gas was raised by # Kelvin/°C with the pressure kept constant?

 

[Simon Bridge]

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.

 

[Flucky]

cool thanks simon

 

[Chestermiller]

A mathematically precise definition of the molar heat capacities which never fails is

C_p=∂H(T,P)/∂T

and

C_v=∂U(T,P)/∂T

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

Chet