Understanding Entropy: From Thermodynamics to Transport Equations

AI Thread Summary
The discussion focuses on deriving expressions for change in entropy based on the second law of thermodynamics and the Stefan-Boltzmann law. It presents a general expression for entropy change, ds = ∮DQ/T, where DQ represents heat transfer and T is the temperature of the reservoir. The conversation delves into specific cases, such as DQ = εσ(Te^4 - Ts^4), leading to the derived expression Ds = (4/3)εσ(Te^3 - Ts^3). Participants express confusion over how to connect these thermodynamic principles and seek further reading on the topic. The relationship between entropy as a thermodynamic property and the Stefan-Boltzmann equation is highlighted as complex and often misunderstood.
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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=\ointDQ/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.
 
Science news on Phys.org
Entropy is a thermodynamic equilibrium property and the Stefan-Boltzmann equation is a transport equation. The two are unrelated.
 

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