# Thermal physics - how are Cp and Cv used?

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?

Simon Bridge
Homework Helper
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.

• 1 person
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?

Simon Bridge
Homework Helper
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.

• 1 person
cool thanks simon

Chestermiller
Mentor
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

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