Is there a relationship between \( k_b \) and \( C_v \)?

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The discussion revolves around the relationship between \( k_b \) (Boltzmann constant) and \( C_v \) (specific heat at constant volume) in the context of a homework problem involving enthalpy. The user has derived an expression for enthalpy but is unsure how to simplify it further. They suggest using the ideal gas law to eliminate pressure-volume terms. The core question remains whether there is a direct relationship between \( k_b \) and \( C_v \). The conversation highlights the need for clarity in simplifying thermodynamic equations.
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Homework Statement



i solved for H=N1Cv1(Tf-T1)+V1(Pf-P1)+N2Cv2(Tf-T2)+V2(Pf-P2)

my TA says that i have to simplify this, i don't really see a good way to go about it

Homework Equations



Pf=(Tf/T1)P1 Pf=(Tf/T2)P2

The Attempt at a Solution

 
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I think you could use the ideal gas law to get rid of the pV terms.
 
so since PV=NkbT

H=N1Cv1(Tf-T1)+N1kb(Tf-T1)+N2Cv2(Tf-T2)+N2kb(Tf-T2)

is there a relationship between kb and Cv?
 

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