Answer
a) $T_4=108.6°C$
b) $\dot{V}=0.0449\ m^3/s$
Work Step by Step
For the turbine:
$\dot{m}_gh_1=\dot{m}_gh_2+\dot{W}_s$
$\dot{W}_s=\dot{m}_gc_p(T_1-T_2)$
$\dot{m}_g=0.02\ kg/s,\ c_p=1.063\ kJ/kg.°C,\ T_1=400\ K,\ T_2=350\ K$
$\dot{W}_s=1.063\ kW$ input to the compressor
For the compressor:
$\dot{W}_s+\dot{m}_ah_3=\dot{m}_ah_4$
$\dot{W}_s=\dot{m}_ac_p(T_4-T_3)$
$\dot{m}_a=0.018\ kg/s,\ c_p=1.008\ kJ/kg.K,\ T_3=50°C$
$T_4=108.6°C$
For the aftercooler:
$\dot{m}_cc_{p,c}(T_{c,e}-T_{c,i})=\dot{m}_ac_{p,a}(T_4-T_5)$
$c_{p,c}=1.005\ kJ/kg.°C,\ T_{c,e}=40°C,\ T_{c,i}=30°C,\ T_5=80°C$
$\dot{m}_c=0.05161\ kg/s$
$\dot{m}=\frac{P\dot{V}}{RT}$
For the cold air inlet:
$P=100\ kPa,\ R=0.287\ kJ/kg.K,\ T=30°C$
$\dot{V}=0.0449\ m^3/s$
