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

Step-by-step 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)[((P_(2))/(P_(1)))^{(R)/(C_(p))} - 1]`

=
`3.5 * 8.314 J/k mol * 306 * [((550)/(125))^{(1)/(3.5)} - 1]`

= 4.692 kJ/mol

Therefore, total work done will be calculated as follows.

Total work done =
`m * W_(s)`

Since, m =
`(150 * 10^(3)g/min)/(29)`. Therefore, putting these values into the above formula as follows.

Total work done =
`m * W_(s)`

=
`(150 * 10^(3)g/min)/(29) * 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 * (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.