Kinetic Theory of Gases

• Units and Variables

• n - number of moles
• R - Universal gas constant
• CV - molar specific heat at constant volume, in J/(mol K)
• CP - 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

• $P=\frac{2}{3}\frac{N}{V}\left(\frac{1}{2}m\stackrel{‾}{{v}^{2}}\right)$
• Average Kinetic Energy per Molecule

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