Concept explainers
a)
The entropy changes and the work input of the compressor per unit mass by treating the propane as an ideal gas variable specific heats.
a)
Answer to Problem 97RP
The work input of the compressor per unit mass by treating the propane as an ideal gas is
The change in entropy per unit mass by treating the propane as an ideal gas is
Explanation of Solution
Refer the table A-2 (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 propane is
Write the formula for entropy change in molar basis at ideal gas state
Here, universal gas constant is
Write the formula for entropy change in mass basis
Refer table A-1, “Molar mass, gas constant and critical properties table”.
The molar mass
Refer the table A-2 (c), “Ideal gas specific heats of various common gases”.
Obtain the empirical constants as follows.
The universal gas constant
Conclusion:
Convert the temperature
Substitute
Substitute
Thus, the work input of the compressor per unit mass by treating the propane as an ideal gas variable specific heats is
Substitute
Equation (III).
Substitute
Thu, the change in entropy per unit mass by treating the propane as an ideal gas variable specific heats is
b)
The entropy changes and the work input of the compressor per unit mass by using departure charts.
b)
Answer to Problem 97RP
The work input of the compressor per unit mass by using enthalpy departure chart is
The change in entropy per unit mass by using entropy departure chart is
Explanation of Solution
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 and change in entropy at ideal state.
Write the formula for change in enthalpy
Here, change in enthalpy of ideal gas is
Write the formula for change in entropy
Here, change in entropy of ideal gas is
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The critical temperature and critical pressure of the propane is as follows.
Refer Table A-2 (a), “Ideal-gas specific heats of various common gases”.
The gas constant
The specific heat at constant pressure
Conclusion:
Substitute
Substitute
Refer Figure A-29, “Generalized enthalpy departure chart”.
The enthalpy departure factor
Refer Figure A-30, “Generalized entropy departure chart”.
The entropy departure factor
Substitute
Substitute
Refer Figure A-29, “Generalized enthalpy departure chart”.
The enthalpy departure factor
Refer Figure A-30, “Generalized entropy departure chart”.
The entropy departure factor
Substitute
Substitute
Here, the work input of the compressor is equal to the enthalpy difference.
Thus, the work input of the compressor per unit mass by using enthalpy departure chart is
Substitute
Substitute
Thus, the change in entropy per unit mass by using entropy departure chart is
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Chapter 12 Solutions
THERMODYNAMICS
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