A molecular beam apparatus employs supersonic jets that allow gas molecules to expand from a gas reservoir held at a specific temperature and pressure into a vacuum through a small orifice. Expansion of the gas results for achieving internal temperatures of roughly 10 K. The expansion can be treated as adiabatic, with the change in gas enthalpy accompanying expansion being converted to kinetic energy associated with the flow of the gas:

The temperature of the reservoir (T_R) is generally greater than the final temperature of the gas, allowing one to consider the entire enthalpy of the gas to be converted into translational motion.

a. For a monatomic gas C_P = 5/2 R. Using this information, demonstrate that the final flow velocity of the molecular beam is related to the initial temperature of the reservoir (T_R) by

b. Using this expression, what is the flow velocity of a molecular beam of Ar where T_R = 298 K? Notice that this is remarkably similar to the average speed of the gas. Therefore, the molecular beam resulting can be described as a gas that travels with velocity but with a very low internal energy. In other words, the distribution of molecular speeds around the flow velocity is significantly reduced in this process.