Air enters a compressor operating at steady state at 1.05 bar, 300 K, with a volumetric flow rate of 30 m3/min and exits at 12 bar, 400 K. Heat transfer occurs at a rate of 5 kW from the compressor to its surroundings. Assuming the ideal gas model for air and neglecting kinetic and potential energy effects, determine the power input, in kW.

power input = -66.2798 kW

Explanation:

Steady state pressure ( Cp ) = 1.05 bar,

Temperature ( T1 ) = 300 K

Volumetric flow rate = 30 m^3/min

exit pressure = 12 bar

exit temperature ( T2 ) = 400 K

Heat transfer rate ( Q ) = 5 kW

Calculate the power input in kW

p1v1 = m RT

m = p1v1 / RT1

   = (1.05 * 10^2 * ( 30/60 )) / ( 0.287 * 300 )

   = 0.60975 m^3/sec

also

h1 + Q = h2 + w

∴ w = m ( h1 - h2 ) + Q  

      = mCp ( t1 - t2 ) + Q ( 1 )

where : ( Q ) = 5 kW ,  Cp  = 1.05 bar, t1 = 300 K,  t2 = 400 k  ( input values into equation 1 )

w = -66.2798 kW

this is true

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