Question

Carbon dioxide gas [M = 44.01 kg/kmol, R = 0.1889 KJ/(kg.K) & T_cr = 304.2 K] is compressed steadily in a water-cooled compressor from P_R1 = 0.15 and T₁ = 365 K to P_R2 = 2 and T₂ = 580 K at a rate of 6 kg/s. The heat rejected to the cooling water is 1058 kW. Using the generalized charts and ideal gas tables, the required power input to the compressor in kW is:

Answer 1

SOLUTION:

Carbon Dioxide gas is being compressed as given in the problem.

Given Data :

M = 44.01 kg/kmol, R = 0.1889 KJ/(kg.K) & T_cr = 304.2 K

P_R1 = 0.15 and T₁ = 365 K to P_R2 = 2 and T₂ = 580 K

= 6 kg/s and heat rejection( ) = 1058 kW

Analysis :

We know from a stasndard table, that Critical pressure  

So

Similarly,  

Now again from the statndard table of Thermophysical Properties of CO2,

at P(1) = 1.1066MPa and T(1) = 365 K , Specific Enthalpy [h(1)] =558.63 kJ/kg

and P(2) = 14.755MPa and T(1) = 580 K , Specific Enthalpy [h(2)] =746.20 kJ/kg

Hense, Work done for compression

So Net Power input to compressor ;

or,