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Summary of ideal gases

Ideal gas equation:

$$$pV=nRT=NkT$$$
  • $$N=nN_{\text{A}}$$
  • $$R=kN_{\text{A}}$$

For Ideal gas : $$U=\frac{3}{2}NkT $$

  • Mean kinetic energy of a gas particle: $$\frac{1}{2}m\langle v^{2}\rangle=\frac{3}{2}kT$$

Root mean square speed of a gas particle:

$$$v_{\text{rms}}=\sqrt{\langle v^{2}\rangle}=\sqrt{\frac{3kT}{m}}$$$

$$p=$$ pressure; $$V=$$ volume; $$n=$$ number of moles; $$m=$$ mass of a particles of gas; $$N=$$ number of particles; $$R=$$ molar gas constant $$(R=8.314\text{ m}^{2}\text{ kg}\text{ s}^{-2}\text{ K}^{-1})$$; $$k=$$ Boltzmann constant $$(k=1.38\times10^{-23}\text{m}^{2}\text{kg s}^{-2}\text{ K}^{-1})$$; $$N_{\text{A}}$$ Avogadro constant $$(N_{A}=6.02\times10^{23})$$; $$T=$$ thermodynamic temperature; $$U=$$ internal energy.