Carbon dioxide enters an adiabatic nozzle at 1200 K with a velocity of 50 m/s and leaves at 400 K. Assuming constant specific heats at room temperature, determine the Mach number at the exit of the nozzle. For CO2 at room temperature (25 °C), R = 188.9 J/kg∙K, cp = 843.9 J/kg∙K, cv = 655 J/kg∙K.

Helium enters a nozzle at 0.5 MPa, 600 K, and a velocity of 120 m/s. Assuming isentropic flow, determine the pressure and temperature of helium at a location where the velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?

Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.6. The pressure and temperature of air are 52 kPa and 270 K, respectively. Now, helium undergoes a normal shock under the same conditions. Calculate the entropy changes of air and helium across the normal shock. The properties of air are R = 0.287 kJ/kg-K and cp= 1.005 kJ/kg-K, and the properties of helium are R=2.0769 kJ/kg-K and cp=5.1926 kJ/kg.K. The entropy change for air is The entropy change for helium is kJ/kg-K. kJ/kg-K.

3. An air stream, which is traveling at a Mach number of 1.8, undergoes a normal shock wave. The stagnation pressure and temperature before the normal shock wave are 150 kPa and 350 K, respectively. Determine a) the temperature and the pressure after the normal shock wave, b) the Mach number and the velocity after the normal shock wave and c) the stagnation temperature and pressure after the shock wave and d) the entropy change across the normal shock wave (Ans. a) 325.4 K, 94.3 kPa, b) 0.6165, 223 m/s, c) 350 K, 122.2 kPa, d) 59.55 J/kgK)