10 mol/s of gas enters a steady state, adiabatic nozzle at T 5 3008C and P 5 5 bar and leaves at T51008C and P 5 1 bar. Find the exiting velocity of the gas if it is: A. Steam B. Nitrogen, modeled as an ideal gas C. An ideal gas with CP 5 (7/2) R and a molecular mass of 28 g/mol.

The answers to the question are

(A) 27.86 m/s

(B) 41.71 m/s

(C) 64.48 m/s

Explanation:

(A) From steam tables we

h1 = 3064.2 kJ/kg and h2 = 2676.2 kJ/kg

With speed, C2 = (2 * (h1-h2)) ^0.5

The speed = 27.86 m/s

(B) Where nitrogen is modelled as an ideal gas we have

T1/T2 = (P1/P2) ^ (Y-1) / Y

Therefore, Y = 3.15 and Cp = Y*R / (Y-1) where R = 0.297 kJ / (kg K, Cp = 0.435

h1 = Cp*T1 = 249.33 kJ/kg

h2 = Cp*T2 = 162.33 kJ/kg

We have 10 moles therefore speed, C2 = (2 * (h1-h2)) ^0.5 = (2 * (249.33 kJ/kg - 162.33 kJ/kg) * 10) ^0.5 = 41.71 m/s

(C) We have R = R'/m = 8314.5 kJ / (g-mol K) / (28 g/mol) = 0.297 kJ / (kg K) and Cp = 7/2*R = 1.0395 kJ / (kg K)

h1 = Cp*T1 = 1.0395 kJ / (kg K) * 573.15 K = 595.79 kJ / (kg) and h2 = Cp*T2 = 387.89 kJ / (kg)

Therefore we have for 10 moles C2 = (2 * (595.79 kJ / (kg) - 387.89 kJ / (kg)) * 10) ^0.5 = 64.48 m/s