Thermal physics - how are Cp and Cv used?

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Discussion Overview

The discussion revolves around the concepts of heat capacities, specifically the differences and applications of Cp (heat capacity at constant pressure) and Cv (heat capacity at constant volume). Participants explore the definitions, relationships, and implications of these heat capacities in various thermodynamic processes.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether Cp and Cv are only applicable in isobaric and isochoric processes, suggesting a potential limitation in their use.
  • Another participant clarifies that the subscripts indicate the state variable held constant and that heat capacities are material properties, not restricted to specific processes.
  • A participant seeks confirmation that a given value for Cp indicates the energy required to raise the temperature of a gas at constant pressure.
  • Further clarification is provided that Cp applies to the entire sample and does not have to be limited to gases, emphasizing the energy used when raising temperature at constant pressure.
  • A precise mathematical definition of Cp and Cv is presented, linking them to enthalpy and internal energy, respectively.

Areas of Agreement / Disagreement

Participants generally agree on the definitions and applications of Cp and Cv, but there is some debate regarding the contexts in which these heat capacities can be applied, particularly concerning isobaric and isochoric processes.

Contextual Notes

Some assumptions about the conditions under which Cp and Cv are measured may not be fully explored, and the implications of different thermodynamic processes on these heat capacities remain unresolved.

Flucky
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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?
 
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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.
 
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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.
 
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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
 
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