The temperature and pressure of air in a large reservoir are $$400$$ $$K$$ and $$3$$ bar respectively. A converging diverging nozzle of exit area $$0.005{m^2}$$ is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is $$50$$ $$kPa.$$ The characteristic gas constant and the ratio of specific heats of air are $$0.287$$ $$kJ/kgK$$ and $$1.4$$ respectively.

The density of air in $$kg/{m^3}$$ at the nozzle exit is

A balloon containing an ideal gas is initially kept in an evacuated and insulated room. The balloon ruptures and the gas fills up the entire room. Which one of the following statements is TRUE at the end of above process?

A rigid, insulated tank is initially evacuated. The tank is connected with a supply line through which air ( assumed to be ideal gas with constant specific heats) passes at $$1$$ $$MPa,$$ $${350^ \circ }C.$$ A valve connected with the supply line is opened and the tank is charged with air until the final pressure inside the tank reaches $$1$$ $$MPa.$$ The final temperature inside the tank.

What is the speed of sound in Neon gas at a temperature of $$500$$ $$K$$ (Gas constant of Neon is $$0.4210$$ $$kJ/kg$$-$$K$$)?