Derivation of Ideal Gas Law

From the Boltzmann equipartition energy theorem, the temperature of the fluid can be written as 

Combining Equations (2.9) and (2.10) and multiplying and dividing the numerator and denominator by the Avogadro number, A,  

the relationship PV=RT for one mole of the gas can be derived. This is the ideal gas law. The assumptions in the box of molecules were in elastic collision, and the gas molecule occupies negligible volume compared to the volume of the container. In Equation (2.11) it can be seen that A is the Avogadro number. A g yields the universal gas constant R (J/mole/K). Eurther, mNIA, gives the number of moles of gas n present in the box. Also, A, P/mN gives the molar volume of the gas. 

Per the phase rule for a pure substance, the number of degrees of freedom can be written as 

FIGURE 2.1 PT diagram of a pure substance (small molecule). 

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Small molecules versus macromolecules Kinetic representation of pressure Derivation of ideal gas law PT diagram of small molecule pure substance PT diagram of polymer van der Waals cubic equation of state Virial equation of state... 

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