Nitrogen gas is compressed from 80 kPa and 27°C to 480 kPa by a 10-kW compressor.

Determine the mass flow rate of nitrogen through the compressor, assuming the compression process to be (a) isentropic, (b) polytropic with n = 1.3, (c) isothermal, and (d) ideal two-stage polytropic with n = 1.3.

The mass flow rate of nitrogen through the compressor, assuming the compression process is as given in each of the options are;

A) m' = 0.047 kg/s

B) m' = 0.051 kg/s

C) m' = 0.062 kg/s

D) m' = 0.056 kg/s

We are given;

Initial Pressure; P₁ = 80 kPa

Final Pressure; P₂ = 480 kPa

Temperature; T₁ =  27 °C = 300 K

Work Input; W = 10 kW

Formula for the mass flow rate is;

where R is ideal gas constant for nitrogen = 0.2968 kJ/kg.K

Plugging in the relevant values gives;

m' = 0.047 kg/s

m' = 0.051 kg/s

plugging in the relevant values gives;

m' = 0.062 kg/s

Plugging in the relevant values gives;

m' = 0.056 kg/s

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