Question

Derive gibbs duhem equation and shows that intensive variables of a system are not independent

Answer 1

Answer:

In thermodynamics, the Gibbs–Duhem equation describes the relationship between changes in chemical potential for components in a thermodynamic system where {\displaystyle N_{i}}N_{i} is the number of moles of component {\displaystyle i,\mathrm {d} \mu _{i}}{\displaystyle i,\mathrm {d} \mu _{i}} the infinitesimal increase in chemical potential for this component, {\displaystyle S}S the entropy, {\displaystyle T}T the absolute temperature, {\displaystyle V}V volume and {\displaystyle p}p the pressure. {\displaystyle I}I is the number of different components in the system. This equation shows that in thermodynamics intensive properties are not independent but related, making it a mathematical statement of the state postulate. When pressure and temperature are variable

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