Question

Carbon dioxide enters an adiabatic compressor at 100 kPa and 300 K at a rate of 0.5 kg/s and leaves at 600 kPa and 450 K. Neglecting kinetic energy changes, determine (a) the volume flow rate of the carbon dioxide at the compressor inlet (b) the power input to the compressor.

Answer 1

Answer:

a)$\dot V = 0.28335 m3/s$

b)$\dot W_{in} = 259.63 kW$

Explanation:

part a)

inlet volume of air V1 is given as $= \frac{RT_1}{P_1}$

putting all value in the above formula

$V_1 = = \frac{0.1889 kpa - m3/kg .K * 300 K}{100kPa}$

$V_1 = 0.5667 m3/kg$

we know that  volume of flow rate

$\dot V = \dot mV_1$

$\dot V = 0.5 kg/s *0.5667 m3/kg = 0.28335 m3/s$

$\dot V = 0.28335 m3/s$

part b

we know that total energy remain constant, so we have

E_in - E_out = Change in energy in system

E_in = E_out

therefore

$\dot W_{in} + \dot m h_1 =\dot m h_2$

$\dot W_{in} = \dot m h_2- \dot m h_1$

the power input to the compressor is

$\dot W_{in} = \dot m c_p (h_2- h_1 )$

$\dot W_{in} = 0.5*5.1926*(450-350 )$

$\dot W_{in} = 259.63 kW$