Question

Nitrogen (N2) at 1 bar, 300 K enters a compressor operating at steady state and is compressed adiabatically to an exit state of 10.5 bar, 645 K. The N2 is modeled as an ideal gas and kinetic and potential energy effects are negligible. Determine the work input, in kJ per kg of N2 flowing, the rate of entropy production, in kJ/K per kg of N2 flowing, and the isentropic compressor efficiency.

Answer 1

Answer:

a)  358.8 KJ/kg

b)  0.0977  KJ/K- kg

c)  83.28%

Explanation:

N2 at 300 k. ( use the properties of N2 at 300 k (T1) )

Cp = 1.04 KJ/kg-k , Cv = 0.743 KJ/Kgk ,  R = 0.1297 KJ/kgk , y = 1.4 ,

Given data:

T2 = 645 k

P1 = 1 bar , P2 = 10.5 bar

a)Determine the work input in KJ/Kg of N2 flowing

Winput = h2 - h1  = Cp( T2 - T1 ) = 1.04 ( 645 - 300 ) = 358.8 KJ/kg

b) Determine the rate of entropy in KJ/K- kg   of N2 flowing

Rate of entropy ( Δs ) = Cp*InT2/T1 - R*In P2/P1

                                    = 1.04 * In (645/300) - 0.1297 * In ( 10.5 / 1 )

                                    = 0.0977  KJ/K- kg

c) Determine isentropic compressor efficiency

Isentropic compressor efficiency = 83.28%

calculated using the relation below

( h'2 - h1 ) / ( h2 - h1 ) = ( T'2 - T1 ) / ( T2 - T1 )

where T'2 = 587.314