Thermal physics - how are Cp and Cv used?

Click For Summary
SUMMARY

The discussion focuses on the definitions and applications of heat capacities, specifically Cp (heat capacity at constant pressure) and Cv (heat capacity at constant volume). The equations provided, including Cp - Cv = nR and Cv = nRf / 2, illustrate the relationship between these capacities and the degrees of freedom (f) of a system. It is clarified that Cp and Cv are material properties and can be utilized in various thermodynamic processes, including adiabatic processes, without the necessity of constant pressure or volume. The molar heat capacities are mathematically defined as Cp=∂H(T,P)/∂T and Cv=∂U(T,P)/∂T, where H is enthalpy and U is internal energy.

PREREQUISITES
  • Understanding of thermodynamic concepts such as heat capacity and degrees of freedom.
  • Familiarity with the laws of thermodynamics and state variables.
  • Knowledge of the relationships between enthalpy (H) and internal energy (U).
  • Basic proficiency in calculus for interpreting the mathematical definitions of heat capacities.
NEXT STEPS
  • Research the implications of heat capacities in various thermodynamic processes.
  • Study the derivation and applications of the equations Cp - Cv = nR and Cv = nRf / 2.
  • Explore the concept of degrees of freedom in thermodynamics and its impact on heat capacity.
  • Learn about the practical applications of Cp and Cv in engineering and material science.
USEFUL FOR

This discussion is beneficial for students and professionals in physics, engineering, and material science, particularly those interested in thermodynamics and heat transfer principles.

Flucky
Messages
93
Reaction score
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?
 
Science news on Phys.org
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.
 
  • Like
Likes   Reactions: 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?
 
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.
 
  • Like
Likes   Reactions: 1 person
cool thanks simon
 
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:

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
16K
  • · Replies 23 ·
Replies
23
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 27 ·
Replies
27
Views
5K
  • · Replies 13 ·
Replies
13
Views
4K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 19 ·
Replies
19
Views
3K