Question

Determine the minimum work required by an air compressor. At the inlet the conditions are 150 kg/min, 125 kPa and 33 °C. At the exit, the pressure is 550 kPa. Assume air is an ideal gas with MW 29 g/mol, Cp 3.5R (constant).

Answer 1

Explanation:

The given data is as follows.

               MW = 29 g/mol,         $C_{p}$ = 3.5 R

Formula to calculate minimum amount of work is as follows.

            $W_{s} = C_{p}T_{1}[(\frac{P_{2}}{P_{1}})^{\frac{R}{C_{p}}} - 1]$

                          = $3.5 \times 8.314 J/k mol \times 306 \times [(\frac{550}{125})^{\frac{1}{3.5}} - 1]$

                          = 4.692 kJ/mol

Therefore, total work done will be calculated as follows.

                        Total work done = $m \times W_{s}$

Since, m = $\frac{150 \times 10^{3}g/min}{29}$. Therefore, putting these values into the above formula as follows.

            Total work done = $m \times W_{s}$

                                        = $\frac{150 \times 10^{3}g/min}{29} \times 4.692 kJ/min$      

                                       = 24268.96 kJ/min

It is known that 1 kJ/min = 0.0166 kW. Hence, convert 24268.96 kJ/min into kW as follows.

                   $24268.96 kJ/min \times \frac{0.0166 kW}{1 kJ/min}$                                                    

                   = 402.86 kW

Thus, we can conclude that the minimum work required by an air compressor is 402.86 kW.