Answer:
- 46.5171kW
Explanation:
FIrst, the value given:
P1 = 1.05 bar (Initial pressure)
P2 = 12 bar (final pressure)
Heat transfer, Q = - 3.5 kW (It is negative because the compressor losses heat to the surroundings)
Mgaseous nitrogen = Mair = 28.0134 Kg/mol (constant)
Universal gas constant, Ru = 8.3143 Kj/Kgmolk
Specific gas constant, R = 0.28699 Kj/KgK
Initial temperature, T1 = 300 K
Final temperature, T2 = 400 K
Finding the volume:
P1V1 = RT1
V1 = RT1 ÷ P1
= (0.28699 Kj/KgK X 300k) ÷ 105
Note convert bar to Kj/Nm by multiply it by 100
V1 = 0.81997 m3/Kg
To get the mass flow rate:
m = volumetric flow rate / V1
= (21 m3/min x 1/60seconds) ÷ 0.81997 m3/Kg
= 0.4268Kg/s
Using tables for the enthalpy,
hT1 = 300.19 KJ/Kg
hT2 = 400.98 KJ/Kg
The enthalpy change = hT2 - hT1
= 100.79 KJ/Kg
Power, P = Q - (m X enthalpy change)
= - 3.5 - (0.4268 X 100.79)
= - 46.5171kW
