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JasonHathaway
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Homework Statement
Air enters a compressor at 100 kPa and 290 K, where it is compressed adiabatically, where the flow rate is 0.1 kg/s. If the volume compression ratio is (V1/V2=8). Determine the following (Assuming the air is ideal with constant specific heat):1- The temperature and the pressure at the exit
2- The compressor’s power in kW
3- The transferred heat amount and the change in entropy
Homework Equations
W` - Q` = m`(∆h + KE + PE)
∆h = m CP (T2 – T1)
P1 V1k= P2 V2k=C
The Attempt at a Solution
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P1 V1k= P2 V2k=C --> (k=1.4 for air)
P2= P1(V1/V2)1.4= 100(8)1.4
P2=1837.9 kPa --> Pressure at exit
Q1-2 = 0 (The process is adiabatic) --> The transferred heat amount
∆s1-2≈ 0 (The process is adiabatic) --> The change in entropy
And we may compute ∆s1-2 using of the these two equations:
∆s1-2= CV ln(T2/T1) + R ln(V2/V1)
∆s1-2= CP ln(T2/T1) - R ln(P2/P1)
W`1-2 = - m` ∆h = m CP (T1 – T2) = (0.1) (1.0035) (290 – 666.23)
W`1-2 = -37.75 kW à The compressor’s power in kw(k, R, CP and Cv are constants we get it from the tables)