Question #151606

Air is compressed from 1 bar , 300 K to 5 bar in a steady flow compressor at the rate of 1200

kg/h. The inlet and outlet pipe diameters are 10 cm each. The rating of compressor is 100

hp. For air, Cp=3.5R, Cv = 2.5R. Assuming ideal gas, estimate the heat transfer rate.

Expert's answer

T1= 27°C 300K

p1= 1 bar

p2= 5 bar

n= (in pvn) 1.2 ( because it is 1200kg/h)

R= 0.287 kJ/kgK

m= 1 kg (to find out per kg of air)

specific heat cv= 0.7175 kJ/kgK

Temperature at the end of compression, T2

compression process 1-2

T2/T1=(p2/P1)^((n-1)/n)

T2/T1= 1.30766

T2= 392.2 K 112.2 °C

Work done and heat transfer during compression per kg of air

work done, W=mRT*(n/n-1)*((p2/p1)^((n-1)/n)-1)

W= - 54.64 kJ/kg of air

Heat transferred during compression, Q=W+ΔU = (p1v1-p2v2)/(n-1)+cv(T2-T1)

Q= (p1v1-p2v2)/(n-1) +cv(T2-T1)= R(T1-T2)/(n-1) + cv(T2-T1)=(T2-T1)*(cv-R/(n-1))

Q= - 198.46 kJ/kg heat rejection

(p1v1-p2v2)*n/(n-1)= -54.64

cv(T2-T1)= 98.4128

Q= (p1v1-p2v2)/(n-1)+cv(T2-T1)= -198.46kJ/kg

cp= 1.0045

mCp(T2-T1)= 92.61

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