Understanding Entropy: From Thermodynamics to Transport Equations

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SUMMARY

This discussion focuses on the derivation and understanding of entropy changes in thermodynamic systems, specifically through the lens of the second law of thermodynamics and the Clausius expression. The key equations presented include the differential change in entropy, ds = ∮DQ/T, and the heat transfer equation DQ = εσ(Te^4 - Ts^4). Additionally, the relationship NRln(Pf/Po) = ds is highlighted, emphasizing the complexity of deriving entropy expressions from the Stefan-Boltzmann law. The discussion concludes with a note on the distinction between entropy as a thermodynamic property and the Stefan-Boltzmann equation as a transport equation.

PREREQUISITES
  • Understanding of the second law of thermodynamics
  • Familiarity with Clausius' expression for entropy
  • Knowledge of the Stefan-Boltzmann law
  • Basic concepts of thermodynamic equilibrium properties
NEXT STEPS
  • Study the derivation of the Clausius inequality in thermodynamics
  • Explore the applications of the Stefan-Boltzmann law in heat transfer
  • Learn about the implications of entropy in thermodynamic cycles
  • Investigate the relationship between entropy and information theory
USEFUL FOR

This discussion is beneficial for physicists, thermodynamics students, and engineers interested in the principles of entropy and heat transfer in thermodynamic systems.

shonen
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From second law of thermodynamics one can obtain an expression for change in entropy of a system developed by Classius.

All thermodynamic systems can be looked at as a reservoir.

ds=[tex]\oint[/tex]DQ/T---(1)

Ds- Change in entropy in the system brought about by reversible heat transfer between system, and surrounding, during some time dt
DQ- Heat transfer either absorbed or removed from system during some time dt.
T- Temperature of reservoir

Now, question is how does one reach from this general expression formed form Stefan-Boltmzman law, corresponding entropy.

DQ=[tex]\epsilon[/tex][tex]\sigma[/tex](Te^4- Ts^4)

Te- Surface Temperature of the surface
Ts- Surface temperature of the body

Ds= 4/3[tex]\epsilon[/tex][tex]\sigma[/tex](Te^3-Ts^3)

Also its puzzling as well how one can obtain this expression as well for how one can obtain the following expression for entropy in this form.

NRln(Pf/Po)=ds

Any recommended reading text will be appreciated.
 
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Entropy is a thermodynamic equilibrium property and the Stefan-Boltzmann equation is a transport equation. The two are unrelated.
 

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