Question

Air enters a compressor operating at steady state at 1.05 bar, 300 K, with a volumetric flow rate of "84" m3/min and exits at 12 bar, 400 K. Heat transfer occurs at a rate of 14 kW from the compressor to its surroundings. Assuming the ideal gas model for air and neglecting kinetic and potential energy effects, determine the power input, in kW.

Answer 1

W = - 184.8 kW

Step-by-step explanation:

Given data:

`P_1 = 1.05 bar`

`T_1 = 300K`

`\dot V_1 = 84 m^3/min`

`P_2 = 12 bar`

`T_2 = 400 K`

We know that work is done as

`W = - [ Q + \dor m[h_2 - h_1]]`

for
`P_1 = 1.05 bar,  T_1 = 300K`

density of air is 1.22 kg/m^3 and
`h_1 = 300 kJ/kg`

for
`P_2 = 12 bar, T_2 = 400 K`

`h_2 = 400 kj/kg`

`\dot m = \rho * \dor v_1 = 1.22 (84)/(60) =1.708 kg/s`

W = -[14 + 1.708[400-300]]

W = - 184.8 kW