Question

Air enters an adiabatic nozzle at 300 kPa, 500 K with a velocity of 10 m/s. It leaves the nozzle at 100 kPa with a velocity of 180 m/s. The inlet area is $80c{m}^2$. The specific heat of air $c_p$ is 1008 J/kgK

The exit temperature of the air is

• A. 516 K
• B. 532 K
• C. 484 K
• D. 468 K

Answer 1

The correct option is C 484 K

Applying the steady flow energy equation
$h_1+\frac{V_1^2}{2}+g{z}_1+q=h_2+\frac{V_2^2}{2}+g{z}_2+w$



Assumption:
$z_1=z_2$
$q=0$, adiabatic flow
$w=0$, always for nozzle
$h_1+\frac{V_1^2}{2}=h_2+\frac{V_2^2}{2}$
$c_p{T}_1+\frac{V_1^2}{2}=c_p{T}_2+\frac{V_2^2}{2}$
$1008\times 500+\frac{(10{)}^2}{2}=1008\times T_2+\frac{(180{)}^2}{2}$
$504050=1008T_2+16200$
or $T_2=483.97K\approx 484K$