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The ideal gas
Ideal gas: ignoring collisions between molecules,
$$
\frac{\normalsize P V}{\normalsize T} = k_B N
$$
Boltzmann's constant: $$k_B = 1.38\times 10^{-23}\quad\frac{\mbox{J}}{\mbox{K}}$$
Avogadro's number: $$N_A = 6.022\times 10^{23}\quad\frac{\mbox{molecules}}{\mbox{mole}}$$
Universal gas constant:
$$R = k_B N_A = 8.31\quad\frac{\mbox{J}}{\mbox{mol K}} = 0.0821\quad \frac{\mbox{l atm}}{\mbox{mol K}}$$
Origin of pressure: collisions of molecules with the walls of the container
Maxwell's velocity distribution:
$$
{K}_{\rm average} = \frac{1}{2} m v_{\rm rms}^2 = \frac{3}{2} k_B T\quad, \qquad
v_{\rm rms} = \sqrt{\frac{\normalsize 3k_BT}{\normalsize m}}
= \sqrt{\frac{\normalsize 3RT}{\normalsize M}}
$$
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