Question

In: Mechanical Engineering

A frictionless air compressor operates between 200 kPa and 6 MPa. The inlet is at 25°C....

A frictionless air compressor operates between 200 kPa and 6 MPa. The inlet is at 25°C. Compared to operating adiabatically, what is the energy-input (e.g. power) savings by cooling it with a polytropic exponent of 1.16? Answer in kJ/kg (i.e. kJ of energy saved for every kg of air compressed).

Correct answer is 9.23 kJ/kg; please show steps and thank you!

Expert Solution

Let the pressure at which air enters the compressor be

The pressure at which air exits the compressor be given as

The inlet temperature of air is

Polytropic index is given as n= 1.16

We are asked to find the savings in power consumption when the compressor operates polytropically incompared to adiabatic(isentropic) manner.

Step1 : Calculating the work when compressor operates isentropically (reversible-adiabatic)

For a isentropic process,

Therefore, temperature of the air at exit of compressor(T2) can be calculated as

(because isentropic index )

Isentropic work input for open flow devices is given as

Therefore,

= 491.70 KJ/Kg .............................................. (1) Isentropic work input(adiabatic)

Step 2: Calculating the polytropic work input,

Lets find the exit temperature of air incase of polytropic work input,

Therefore, temperature of the air at exit of compressor(T2) can be calculated as

Now, polytropic work for open flow devices is given as

= 371.1704 KJ/kg .......................................(2) (Polytropic work input)

Step 3: Calculating the savings:

The savings in power consumption is

Note: Above is the correct answer, the one provided in question is wrong. Please upvote if you find my solution to be useful, Good luck!!

We were unable to transcribe this image

Ti = 25 C = 298K

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samet mamat answered 2 months ago

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