Question #175244

An adiabatic expansion of air occurs through a nozzle (W1=0) from 850 kPa and 75C to 140 kPa. For an isentropic expansion find: specific volume(m/kg), temperature(C) and velocity(m/s) at the exit section assuming initial kinetic energy is negligible

Expert's answer

The inlet temperature(T1)= 75 C=75+273=348 K

Inlet Pressure(P1)=850 x 10^{3} Pa

The exit Pressure(P2)=140x10^{3}Pa

Assuming air as ideal gas having following properties:

Cp = 1.004 kJ/kg.K, Cv = 0.718 kJ/kg.K, k = 1.4 and R=0.287 kJ/kg K

Since the expansion is adiabatic,

"\\frac{T_2}{T_1}={\\frac{P_2}{P_1}}^{\\frac{K-1}{K}}"

"\\frac{T_2}{348}={[\\frac{140}{850}]}^{\\frac{1.4-1}{1.4}}"

"T_2=207.865 K"

specific volume at exit is given by,

"v_2=\\frac{{RT_2}}{P_2}\\\\v_2=\\frac{{287\\times 207.86}}{140000}=0.426kg\/m^3"

In an adiabatic turbine there is no Heat or work transfer between system and surrounding,

W=0, Q=0

Applying steady flow energy equation between inlet and exit."\\ h_1+\\frac{V^2_1}{2}=h_2+\\frac{V^2_2}{2}"

At inlet velocity of flow is negligible,

=> V_{1}=0

The velocity at exit is given by,

"{V_2}=\\sqrt{h_1-h_2}"

"{V_2}=\\sqrt{C_p(T_1-T_2)}=\\sqrt{1.004\\times (348-207.865)\\times1000}=375.09\\space m\/s"

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