Cp and Cv under the kinetic theory
Since ideal gas is very dilute, molecules are far apart, and gravitational forces between them are small.
• Internal energy of an ideal gas is sum of molecular kinetic and potential energies
• Since ideal gas is very dilute, molecules are far apart, and gravitational forces between them are small.
• If we change the volume (i.e. density), the distance between the molecules changes, and the potential energy changes. However, since this change is extremely small for an ideal gas, this change does not have an effect on internal energy.
• Thus, for ideal gas, internal energy is only dependent on kinetic energy of molecules.
• The molar internal energy
• Now, what about a diatomic gas?
• Monatomic gas has 3 degrees of freedom (i.e. one must specify 3 independent quantities to determine the energy, in this case Vx, Vy, and Vz)
Equipartition of Energy Principle:
“Total energy of molecules is divided equally among all degrees of freedom.”
• Thus, monatomic gas has 3 degrees of freedom, each with of energy, for a total energy of
• Each additional degree of freedom must contribute to total energy. Thus, the molar internal energy is
for f degrees of freedom.