[Thermal] Is it possible that increases of moles decrease entropy?

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SUMMARY

The discussion centers on the relationship between the number of moles in a system and its entropy, as described in "Statistical and Thermal Physics" by Reif (1985). The entropy formula presented indicates that while increasing temperature and volume leads to higher entropy, there exists a threshold where increasing moles can actually decrease entropy. This counterintuitive behavior suggests a complex interplay between these variables that warrants further investigation.

PREREQUISITES
  • Understanding of thermodynamic principles, particularly entropy.
  • Familiarity with the concepts of specific heat and its role in thermodynamics.
  • Knowledge of statistical mechanics as outlined in "Statistical and Thermal Physics".
  • Basic calculus for interpreting integrals in thermodynamic equations.
NEXT STEPS
  • Research the implications of the entropy formula S(T,V;√) in various thermodynamic systems.
  • Explore the concept of specific heat (cv) and its impact on entropy changes.
  • Investigate the conditions under which increasing moles leads to decreased entropy.
  • Study advanced topics in statistical mechanics to understand the behavior of systems at different thermodynamic limits.
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Students and professionals in physics, particularly those focused on thermodynamics and statistical mechanics, as well as researchers exploring the nuances of entropy in physical systems.

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From Statsitical And Thermal Physics (Reif. international edition 1985)

160 page. (5.4.4)

S(T,V;√) = √[∫{cv(T`)/T`}dT` + Rln(V) - Rln(√) + constant]

(integral is from T0 to T , cv is specific heat)


This is a entropy of system for temperature 'T' , Volume 'V' , Moles '√' <-- this is mu

as you see, by increasing volume and temperature, entropy increases (trivial)

but by fixing other variables except for moles,

there is some extreme max value.

i.e. entropy gets lowered by incresing moles from some point.

ps. Is there any way that I can upload my photo file in my computer?

I expected increases of moles makes entropy higher.

What is the problem??
 
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