Project ForgeThermodynamics
First Law of Thermodynamics
GATE 2012
Hard
For the same adiabatic nozzle described above (air enters at 300 kPa, 500 K, 10 m/s through an inlet area of 80 cm²; leaves at 100 kPa, 180 m/s, with exit temperature 484 K as found from the energy balance; Cp=1008 J/kg.K, use R=287 J/kg.K for air), the exit area of the nozzle in cm² is
- A90.1
- B56.3
- C4.4
- 12.9
Explanation
Inlet density ρ1=P1/(RT1)=300000/(287×500)=2.091 kg/m³. Mass flow ṁ=ρ1A1V1=2.091×0.008×10=0.1673 kg/s. Exit density ρ2=P2/(RT2)=100000/(287×484)=0.7200 kg/m³. Exit area A2=ṁ/(ρ2V2)=0.1673/(0.7200×180)=0.001291 m²=12.9 cm².
Source: GATE ME 2012 (Booklet Code A) (2012)
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