Kinetic theory of gases

Kinetic Theory of Gases

• Units and Variables

  • n - number of moles
  • R - Universal gas constant
  • C_V - molar specific heat at constant volume, in J/(mol K)
  • C_P - molar specific heat at constant pressure, in J/(mol K)
• $R=8.314472\frac{J}{K\mathrm{mol}}$
• $C_V=\frac{3}{2}R$
• $C_P=\frac{5}{2}R$
• $R=C_P-C_V$
• $\gamma =\frac{C_P}{C_V}$

• Relationship between pressure and volume for an adiabatic process

  • $P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$

• Relationship between volume and pressure for an adiabatic process

  • $T_1{V}_1^{\left(\gamma -1\right)}=T_2{V}_2^{\left(\gamma -1\right)}$

• Relationship between pressure and molecular kinetic energy

  • $P=\frac{2}{3}\frac{N}{V}\left(\frac{1}{2}m\overline{v^2}\right)$

• Average Kinetic Energy per Molecule

  • $\frac{1}{2}m\overline{v^2}=\frac{3}{2}{k}_{B}T$
• $E_{\mathrm{int}}=\frac{3}{2}{k}_{B}T=\frac{3}{2}nRT$