Thermodynamics: Air compressor

[JasonHathaway]

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 V1^k= P2 V2^k=C

The Attempt at a Solution

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P1 V1^k= P2 V2^k=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)

 

[anathema]

Overall, your attempt at a solution looks good. You correctly used the adiabatic compression equation to find the pressure at the exit and determined that there is no heat transfer and change in entropy due to the process being adiabatic. You also correctly used the equations for work and change in entropy to find the compressor's power and change in entropy.

One thing to note is that the specific heat values you used (1.0035 and 1.4) may not be the most accurate for air at these conditions. It would be better to use the specific heat values at the average temperature of 290 K, which can be found in tables or calculated using the average temperature formula (T_avg = (T1+T2)/2). This may slightly change your results, but overall your approach is correct.

Another thing to consider is the units of the compressor's power. It is typically expressed in Watts (W) rather than kW. To convert from kW to W, you would need to multiply by 1000.

Overall, great job on your solution!