Where Does the Entropy Formula Come From in Thermodynamics?

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SUMMARY

The entropy formula in thermodynamics, expressed as dS = (∂S/∂T)_P(dT) + (∂S/∂P)_T(dP), arises from the general principles of differentiation for functions of multiple variables. The discussion highlights that the entropy function S can be expressed in terms of temperature (T) and pressure (P) as independent variables. The derivation is straightforward, relying on the application of partial derivatives rather than complex physical concepts.

PREREQUISITES
  • Understanding of Maxwell thermodynamic relations
  • Familiarity with partial differentiation
  • Basic knowledge of thermodynamic variables such as temperature and pressure
  • Concept of state functions in thermodynamics
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  • Study the derivation of Maxwell's relations in thermodynamics
  • Learn about the implications of state functions in thermodynamic systems
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Master J
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Hey guys.

Right, I have been studying the Maxwell thermodynaic relations. But I have come across entropy as

dS = (bS/bT)_P(dT) + (bS/bP)_T(dP)

where b is the partial differential symbol.

I don't understand where this comes from, which suggests S(T,P). I can't find a derivation of this.

Could you help?
 
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It's nothing really to derive. Physically, I mean.
For any function of two variables, the general formula for differentiation looks like this.
I mean, for f(x,y)
df=(bf/bx)dx+(bf/by)dy.

As for why S(p,T), you can use any two independent variables as "dependent variables".
 

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