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.
a)
The mass flow rate of nitrogen through the compressor for isentropic compression process
Answer to Problem 111P
The mass flow rate of nitrogen through the compressor for isentropic compression process is
Explanation of Solution
Write the expression for the power input of the compressor for isentropic compression process.
Here, power input of the compressor is
Conclusion:
From Table A-1, “Ideal-gas specific heats of various common gases”, the value of gas constant
From Table A-2, “Ideal-gas specific heats of various common gases”, the value of specific heat ratio
Substitute 10 kW for
Thus, the mass flow rate of nitrogen through the compressor for isentropic compression process is
b)
The mass flow rate of nitrogen through the compressor for polytropic compression process.
Answer to Problem 111P
The mass flow rate of nitrogen through the compressor for polytropic compression process is
Explanation of Solution
Write the expression for the the power input of the compressor for polytropic compression process.
Here, power input of the compressor is
Conclusion:
Substitute 10 kW for
Thus, the mass flow rate of nitrogen through the compressor for polytropic compression process is
c)
The mass flow rate of nitrogen through the compressor for isothermal compression process.
Answer to Problem 111P
The mass flow rate of nitrogen through the compressor for isothermal compression process is
Explanation of Solution
Write the expression to calculate the power input of the compressor for isothermal compression process.
Here, power input of the compressor is
Conclusion:
Substitute 10 kW for
Thus, the mass flow rate of nitrogen through the compressor for isothermal compression process is
d)
The mass flow rate of nitrogen for two stage compression process.
Answer to Problem 111P
The mass flow rate of nitrogen for two stage compression process is
Explanation of Solution
Write the expression to calculate the even pressure or pressure ratio
Write the expression to calculate the power input of the compressor for two stage compression process.
Here, power input of the compressor is
Conclusion:
Substitute
Substitute 10 kW for
Thus, the mass flow rate of nitrogen for two stage compression process is
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