A supersonic nozzle is a cone-shaped object with a small hole in the end through which a gas is forced. As the gas moves through the nozzle opening, the gas expands in a manner that can be approximated as reversible and adiabatic. Such nozzles are used in molecular beams and in supersonic aircraft engines to provide a thrust, because as the gas cools (in an adiabatic expansion), its random thermal energy is converted into directed motion of the molecules with average velocity v . Little thermodynamic work is done because the external pressure is low; thus, the net effect is to convert thermal energy to net translational motion of the gas molecules. Suppose the gas in the nozzle is helium; its pressure is 50 atm and its temperature is 400 K before it begins its expansion. (a) What are the average speed (magnitude) and the average velocity (vector with direction) of the molecules before the expansion. (b) Treat helium as a monoatomic ideal gas. What will be the temperature of the gas after its pressure has decreased to 1.0 atm in the (adiabatic) expansion? (c) What is the average speed of the molecules in their random thermal motions? What is the change in random thermal energy (per mole) of He that goes through the nozzle? This amount of energy appears as kinetic energy of directed motion of the expelled helium. This macroscopic, non-thermal kinetic energy belongs to the whole parcel of helium as it travels away from the nozzle. What is the velocity of the parcel, which is also the average velocity of the molecules that compose it? Verify if the motion of the expelled helium is indeed supersonic or not. The speed of sound in dry air at room conditions is about 350 m s-1 .