Carbon dioxide enters an adiabatic compressor at 100 kPa and 300K at a rate of 0.5 kg/s and leaves at 600 kPa and 450K. Neglecting kinetic energy changes, determine a) the volume flow rate of the carbon dioxide at the compressor inlet (Ans. around 0.3 m3/s) and b) the power input to the compressor (Ans. around 70 kW).

The answers to the question are

a) The volume flow rate of the carbon dioxide at the compressor inlet is 0.2834 m³/s ≈ 0.3 m³/s

b) The power input to the compressor is 73.35 kW ≈ 70 kW

Explanation:

We note the following

Mass flow rate = 0.5 kg/s

Inlet pressure = 100 pKa

Outlet pressure = 600 kPa

Inlet temperature = 300 K

Outlet temperature  =  450 K

Molar mass of CO₂ = 44.01 g/mol

R Universal Gas Constant = 8.314 4621. J K−1 mol−1

a) Number of moles = = = 11.361 moles

P·V= n·R·T ∴ V = = = 0.2834 m³

Therefore the volume flow rate = 0.2834 m³/s ≈ 0.3 m³/s

b) Cp at 300 K = 0.846 kJ/(kg K)

Cp at 600 K = 0.978 kJ/(kg K)

Cv = 0.657

K = 1.289

While the power input to the compressor can be calculated by

m'×Cp×(T₂-T₁)

Where m' = mass flow rate = 0.5 kg/s

Therefore power = 0.5 kg/s×0.978 kJ/(kg K)×(450 K - 300 K)

= 73.35 kJ/s = 73.35 kW ≈ 70 kW