Concept explainers
Helium gas is compressed from 16 psia and 85°F to 120 psia at a rate of 10 ft3/s. Determine the power input to the compressor, assuming the compression process to be (a) isentropic, (b) polytropic with n = 1.2, (c) isothermal, and (d) ideal two-stage polytropic with n = 1.2.
a)
The power input of the compressor for isentropic compression process
Answer to Problem 110P
The power input of the compressor for isentropic compression process is
Explanation of Solution
Write the expression to calculate the mass flow rate
Here, initial pressure is
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-2E, “Ideal-gas specific heats of various common gases”, the value of gas constant
Substitute
Substitute
Thus, the power input of the compressor for isentropic compression process is
b)
The power input of the compressor for polytropic compression process.
Answer to Problem 110P
The power input of 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
Thus, the power input of the compressor for polytropic compression process is
c)
The power input of the compressor for isothermal compression process.
Answer to Problem 110P
The power input of 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
Thus, the power input of the compressor for isothermal compression process is
d)
The expression to calculate the power input of the compressor for two stage compression process
Answer to Problem 110P
The expression to calculate the power input of the compressor 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
Thus, the expression to calculate the power input of the compressor for two stage compression process is
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Chapter 7 Solutions
Thermodynamics: An Engineering Approach ( 9th International Edition ) ISBN:9781260092684
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