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 and (b) the power input to the compressor. Amswers: (a) 0.283 m^3/s, (b) 68.8 kW

Answer 1

Answer:

(a) $Q_1=0.283m^3/s$

(b) $W=68.8kW$

Explanation:

Hello,

(a) Based on the inlet conditions, we see that such carbon dioxide has an ideal behavior, so the inlet specific volume is:

$v_1=\frac{RT}{PM}=\frac{8.314\frac{Pa*m^3}{mol*K}*300K}{100000Pa*44g/mol} =0.000567m^3/kg$

Thus, the volumetric flow rate turns out:

$Q_1=0.000567m^3/g*0.5kg/s*1000=0.283m^3/s$

(b) Now, by writing and energy balance we have:

$mh_1+W=mh_2$

Thus, since the ideal gas enthalpy does not depend on the pressure, in Cengel's A-20 table, the corresponding enthalpies at 300K and 450 K are 9431kJ/kmol and 15483kJ/kmol whose values in kJ/kg are 214.34 kJ/kg and 351.89 kJ/kg respectively, thus:

$W=0.5kg/s*(351.89-214.34)kJ/kg=68.8kW$

Best regards.