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
<u>A) Determine the minimum theoretical power input required and exit temp </u>
<em>i) Exit temperature :</em>
∴ = ( 37 + 273 ) *
= 592.2 k
i<em>i) Theoretical power input :</em>
W =
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 )
<u>B) Determine power input and Isentropic compressor efficiency </u>
Given Temperature = 3978C
<em>i) power input to compressor</em>
W = m* ( 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
<em>ii) compressor efficiency </em>
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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