Derivation of thermodynamics
- For deriving thermodynamics we consider that the system is under quasi-static thermodynamic transformation.
- A quasi-static thermodynamic transformation corresponds to a slow variation of E and V, induced by coupling the system to external agents.
- The variation is so slow that at every instant we have a microcanonical ensemble.
- Since S = S (E, V)
- So the change in entropy in an infinitesimal small transformation is
or T dS = dE + P dV
or dE = T dS – P dV
- This is first law of thermodynamics.
- Thus by using classical statistical mechanics we can derive first and second law of thermodynamics i.e.,
dE = T dS – P dV and dE = T dS
- and also all thermodynamic function in terms of molecular interaction.
- Third law of thermodynamics can be obtained by quantum mechanical statistics.
How can we find all the thermodynamic function of a system
- Consider an isolated system having volume V and energy E within a small uncertainty ΔE << E
(i) Calculate the density of state ω(E) of the system by using
(ii) Find the entropy by
(iii) Find E from above equation in terms of S and V. The resulting function is the thermodynamic internal energy of the system i.e., U
∴ U (S, V) = E (S, V)
(iv) From U, other thermodynamic function can be derived as
- To know more about derivation of thermodynamics click on the link for English and click on the link for Hindi
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