Question

Example 6: Find the minimum energy required to compress one kg of air from 15°C and 1 bar to 40 bar in 2-stage compressor. The law of compression is pV ^ 1.25 = constant, and intercooling is perfect.​

Answer 1

Given:-

1 Kg of air which have to compress and the given temperature is 15°C and the pressure is 1 bar to 40 bar it is  in a second stage compressor. And The law of compression is PV^1.25 = constant and intercooling is perfect

To Find :-

The minimum energy required to compress 1Kg of air

Solution:-

For calculating the minimum energy for the compression of 1 kg air we have to use the following expression

E =  2n/n-1 * m*R*T[ (P2/P1)^n-1/2n -1]

here , P1 = 1 bar = 1 *10^2 kN/m^2

     P2 = 40 bar = 40*10^2 kN/m^2

•   T1 = 15°C = 288K and the law of compression PV^1.25 = C ,means it is  a polytropic compression process ( n= 1.25) , mass m= 1Kg , R is the gas constant here we have to use the value 0.287 KJ/Kg.K for air

• Now put all the values in the above expression we get

    E = 2* 1.25/1.25-1 * 1Kg * 0.287 * 288[ (4*10^3/10^2)^1.25-1/2*1.25  - 1]

 =>   2.50/0.25 * 0.287 * 288 [ (4)^0.25/2.50  - 1]

=>   10* 0.287 * 288 [ (4)^0.1 -1 ]

=>   2.87 * 288 * 0.14 =>  115.71 kW

So the required minimum energy to compress 1 kg of air is 115.71 kW