Explain the Thermodynamic Identities ?

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Explain the Thermodynamic Identities ?

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The relations between Thermodynamics term (eg. entropy, temperature, internal energy, heat, etc.) known as Thermodynamic identity. The equation may have more than one state or path variables are present. Thermodynamic identities always true for any infinitesimal changes in thermodynamic system. The changes may be pressure, temperature or volume or any other kind.

dU=TdS-PdV

Helmholtz free energy:

F=U-TS

dF = dU-TdS-SdT

dF=-PdV-SdT+μdN

Gibbs free energy

dG = −SdT + VdP + µdN

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