Question

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

Answer 1

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

Inlet Pressure(P1)=850 x 10³ Pa

The exit Pressure(P2)=140x10³Pa

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,

=> V₁=0

The velocity at exit is given by,

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

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