Question

Deduce the relation $$PV = nRT$$, where $$R$$ is a constant called universal gas constant.

Answer 1

According to Boyle’s law, $$V\ \alpha\ \dfrac{1}{P}$$ (at constant $$T$$ and $$n$$)

According to Charle’s law, $$V\ \alpha\ \dfrac{1}{T}$$ (at constant $$P$$ and $$n$$)

According to Avogadro's law, $$V\ \alpha\ n$$ (at constant $$T$$ and $$P$$)

Combining the three laws, $$V\ \alpha\ \dfrac{nT}{P}$$ or $$PV\ \alpha\ nRT$$

Or $$PV = nRT$$ where $$R$$ is a constant called universal gas constant.