Start from the four fundamental equations full differentials...

Start from the four fundamental equations (full differentials of U, H, A, and G) for one mole of a closed simple system (Consider P-V work only), and derive four Maxwell's relations.

Transcript

00:01 Hello students in the first part of this question we need to explain the four thermodynamic potentials that is first one is the internal energy the internal energy is defined as sum of kinetic and potential energies of all the particles in the system and it can be represented as a function of u equal to u of s and v where s is the entropy of the system and v volume is the of the system now second potential is enthalpy that is it is defined as h is equal to u plus pv where u is internal energy p is pressure and molium represent it represents the total heat content of a system at constant pressure now third one is a helmholtz free energy represented as f it is defined as f is equal to u minus ts u is internal energy t is temperature and s is entropy where it represents a maximum amount of work that can be extracted from a system at constant temperature and hold him now the fourth one is gibbs free energy g that is g can be represented as h is h g is equal to h minus ts that is it represents a maximum amount of work that can be extracted from a system at constant temperature and pressure now for the second part we need to say the differentials of each thermodynamic potential so the internal energy du is equal to tds minus pdv and enthalpy dh is equal to tds plus vdp and the helmholtz free energy df is equal to minus pdv minus sdt and the gibbs free energy dg is equal to vdp minus sdt now as a third part of the question we need to derive the maxwell's 4 relation that is first one is we are deriving it from the equation of internal energy that is du equal to tds minus pdv so u is a function of s and v now the equation of u can be written as taking the partial derivative dou u by dou s at constant v at ds plus dou u by dou v at s dv so consider it as equation 2 and this one as the equation 1 now comparing equation 1 and 2 we can write dou u by dou s at v is equal to t and dou u by dou v at s is equal to minus p now differentiating with respect to v we can say that dou by dou v of dou u by dou s at constant v at constant entropy s is equal to dou by dou s of dou u by dou v at s and this is at v so here we can simply write the relation as dou t by dou v at constant s is equal to minus of dou p by dou s so this is the first relation of maxwell and this is from internal energy now to derive the second relation with we are doing it from the helmholtz free energy h that is we can write as df is equal to minus pdv minus sdt considering it as…

Question

Start from the four fundamental equations (full differentials of U, H, A, and G) for one mole of a closed simple system (Consider P-V work only), and derive four Maxwell's relations.

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