Understanding Entropy: From Thermodynamics to Transport Equations

[shonen]

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=$$\oint$$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=$$\epsilon$$$$\sigma$$(Te^4- Ts^4)

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

Ds= 4/3$$\epsilon$$$$\sigma$$(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.

 

[Chestermiller]

Entropy is a thermodynamic equilibrium property and the Stefan-Boltzmann equation is a transport equation. The two are unrelated.