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. Neglec

Question

1 year ago

3

ting kinetic energy changes, determine (a) the volume flow rate of the carbon dioxide at the compressor inlet (b) the power input to the compressor.

1 answer:

ra1l [238] · Answer 1 · 2020-07-16T11:07:13+03:00

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

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

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

$\dot W_{in} = 259.63 kW$