Kinetic Theory of Sound for a Polyatomic Gas

The initial‐value problem is studied for an unbounded gas whose molecules possess internal energy states. A relaxation model is used to approximate the Wang Chang‐Uhlenbeck generalization of the Boltzmann collision integral for a polyatomic gas. The model depends on two adjustable parameters, the elastic and inelastic relaxation times. The problem gives some insight into the behavior of the collective modes of motion of the gas. For linear molecules permitted rotational but not vibrational degrees of freedom the model predicts corrections to the adiabatic sound velocity of ${\text{(7kT/5m)}}^{\frac{1}{2}}$ in the near continuum limit. The absorption as well as purely dissipative modes are obtained as functions of the elastic and inelastic relaxation times.