Nitrogen (N2) enters an insulated compressor operating at steady state at 1 bar, 378C with a mass flow rate of 1000 kg/h and exits at 10 bar. Kinetic and potential energy effects are negligible. The nitrogen can be modeled as an ideal gas with k 5 1.391. (a) Determine the minimum theoretical power input required, in kW, and the corresponding exit temperature, in 8C. (b) If the exit temperature is 3978C, determine the power input, in kW, and the isentropic compressor efficiency.

Answer:

A)

i) 592.2 k

ii) - 80 kw

B)

i) 105.86 kw

ii) 78%

Explanation:

Note : Nitrogen is modelled as an ideal gas hence R - value = 0.287

A) Determine the minimum theoretical power input required  and exit temp

i) Exit temperature :

[tex]\frac{T_{2s} }{T_{1} } = (\frac{P2}{P1} )^{\frac{k-1}{k} }[/tex]

∴ [tex]T_{2s}[/tex]  = ( 37 + 273 ) * [tex](\frac{10}{1} )^{\frac{1.391-1}{1.391} }[/tex]  =  592.2 k

ii) Theoretical power input :

W = [tex]\frac{-n}{n-1} mR(T_{2} - T_{1} )[/tex]

where : n = 1.391 , m = 1000/3600 , T2= 592.2 , T1 = 310 , R = 0.287

W = - 80 kW  ( i.e. power supplied to the system )

B) Determine power input and Isentropic compressor efficiency

Given Temperature = 3978C

i) power input to compressor

W = m* [tex]\frac{1}{M}[/tex] ( h2 - h1 )

h2 = 19685 kJ/ kmol ( value gotten from Nitrogen table at temp = 670k )

h1 = 9014 kj/kmol ( value gotten from Nitrogen table at temp = 310 k )

m = 1000/3600 ,  M = 28

input values into equation above

W = 105.86 kw

ii) compressor efficiency

П = ideal work output / actual work output

   = ( h2s - h1 ) / ( h2 - h1 ) = ( T2s - T1 ) / ( T2 - T1 )

  = ( 592.2 - 310 ) / ( 670 - 310 )

  = 0.784 ≈ 78%

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