Question

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).

Answer 1

Explanation:

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Answer 2

Answer:

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 = $\frac{Mass}{Molar.Mass}$ = $\frac{500g}{44.01g}$ = 11.361 moles

P·V= n·R·T ∴ V = $\frac{n*R*T}{P}$ = $\frac{11.361*8.3145*300}{ 100 }$ = 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