Concept explainers
Methane is to be adiabatically and reversibly compressed from 50 psia and 100°F to 500 psia. Calculate the specific work required for this compression treating the methane as an ideal gas with variable specific heats and using the departure charts.
FIGURE P12–96E
The work input of the compressor per unit mass by treating the methane as an ideal gas with variable specific heats and using departure charts.
Answer to Problem 96RP
The work input of the compressor per unit mass by treating the methane as an ideal gas with variable specific heats is
The work input of the compressor per unit mass of the methane using departure charts is
Explanation of Solution
Refer the table A-2E (c), “Ideal gas specific heats of various common gases”.
The general empirical correlation is
Write the formula for enthalpy change in molar basis at ideal gas state
Here, specific heat capacity at constant pressure is
Write the formula for work input to the compressor
Here, molar mass of methane is
Write the formula for entropy change in molar basis at ideal gas state
Here, universal gas constant is
Calculate the reduced temperature
Here, critical temperature is
Calculate the reduced pressure
Here, critical pressure is
Calculate the reduced temperature
Here, critical temperature is
Calculate the reduced pressure
Here, critical pressure is
Write the formula for change in enthalpy
Here, change in enthalpy of ideal gas is
Refer Table A-1E, “Molar mass, gas constant, and critical-point properties”.
The critical temperature and critical pressure of the methane is as follows.
Refer table A-1E, “Molar mass, gas constant and critical properties table”.
The molar mass
Refer the table A-2E (c), “Ideal gas specific heats of various common gases”.
Obtain the empirical constants as follows.
Refer Table A-2E (a), “Ideal-gas specific heats of various common gases”.
The gas constant
The specific heat at constant pressure
The universal gas constant
Conclusion:
Convert the inlet temperature from degree Fahrenheit to Rankine.
It is given that the compression process in reversible adiabatic process. Hence, the change in entropy during the process is zero.
Substitute
By using Engineering Equation Solver (EES) or online calculator to solve the Equation (XI) and obtain the value of
Substitute
Substitute
Thus, the work input of the compressor per unit mass by treating the methane as an ideal gas with variable specific heats is
Substitute
Substitute
Refer Figure A-29, “Generalized enthalpy departure chart”.
The enthalpy departure factor
Consider the final temperature
Substitute
Substitute
Refer Figure A-29, “Generalized enthalpy departure chart”.
The enthalpy departure factor
Substitute
Here, the work input of the compressor is equal to the enthalpy difference.
Thus, the work input of the compressor per unit mass of the methane using departure charts is
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