Ideal Gas Partition: Final Temp & Total Energy Change

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SUMMARY

The discussion focuses on the thermodynamic analysis of two ideal gases separated by a partition, specifically addressing the calculation of final temperature and total energy change. For part a, the final temperature Tf is determined to be (T1 + T2) / 2 when N1 = N2 and V1 = V2. The user seeks assistance with parts b and c, which involve evaluating changes in quantities H and A, respectively, using the provided differential equations. The internal energy U is defined as U = NVCv dT, which is crucial for solving the subsequent parts.

PREREQUISITES
  • Understanding of ideal gas laws and properties
  • Familiarity with thermodynamic concepts such as internal energy and specific heat
  • Knowledge of differential calculus in the context of thermodynamics
  • Ability to manipulate equations involving multiple variables
NEXT STEPS
  • Study the derivation of the final temperature for systems with multiple ideal gases
  • Learn about the first law of thermodynamics and its application to energy changes
  • Explore the concept of enthalpy and its differential form dH = dU + Vdp
  • Investigate the differential change in Helmholtz free energy, particularly dA = (dU + pdV)/T
USEFUL FOR

This discussion is beneficial for students and professionals in thermodynamics, particularly those studying or working with ideal gases, energy changes in thermodynamic systems, and related calculations in physics or engineering.

oxman
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Two ideal gases are separated by a partition which does not allow molecules to pass from one volume to the other. Gas 1 has: N1, V1, T1, Cv1 for the number of molecules, volume it occupies, temperature in kelvin, and specific heat per molecule at constant volume respectively. Gas 2 has: N2, V2, T2, Cv2. The two gases are in thermal contact and reach a final temperature

a) find the final temperature and the total change in energy of the combined system. Check your answer for the final temperature when N1=N2, V1=V2. Cv1=Cv2

b)Evaluate the total change ina quantity H whose differential change is dH=dU+Vdp for each component and for the entire system

c)evaluate the total change in a quantity A whose differential change is dA=(dU+pdV)/T for each component and for the entire system

I am having trouble with b and c

U=NVCvdT

I already solved for the final temperature for part a, and when evaluated at equal N and V i got Tf=(T2+T1)/2
 
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