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

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SUMMARY

The discussion centers on the relationship between \( k_b \) (Boltzmann's constant) and \( C_v \) (specific heat at constant volume) in the context of thermodynamics. The user presents an equation for enthalpy \( H \) involving \( N_1, C_{v1}, T_f, T_1, V_1, P_f, P_1, N_2, C_{v2}, T_2, V_2, P_2 \) and seeks to simplify it. The user suggests utilizing the ideal gas law, represented as \( PV = N k_b T \), to eliminate pressure-volume terms from the equation. The inquiry specifically asks for a definitive relationship between \( k_b \) and \( C_v \).

PREREQUISITES
  • Understanding of thermodynamic concepts such as enthalpy and specific heat
  • Familiarity with the ideal gas law and its applications
  • Knowledge of variables involved in thermodynamic equations (e.g., \( N, P, V, T \))
  • Basic algebraic manipulation skills for simplifying equations
NEXT STEPS
  • Research the derivation of the relationship between \( k_b \) and \( C_v \) in thermodynamics
  • Study the implications of the ideal gas law on thermodynamic properties
  • Explore advanced thermodynamic equations and their simplifications
  • Learn about the role of specific heat in different thermodynamic processes
USEFUL FOR

Students and professionals in physics and engineering, particularly those studying thermodynamics and heat transfer, will benefit from this discussion.

oxman
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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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