Concept explainers
A piston–cylinder device initially contains 15 ft3 of helium gas at 25 psia and 70°F. Helium is now compressed in a polytropic process (PVn = constant) to 70 psia and 300°F. Determine (a) the entropy change of helium, (b) the entropy change of the surroundings, and (c) whether this process is reversible, irreversible, or impossible. Assume the surroundings are at 70°F.
a)
The change in entropy of helium.
Answer to Problem 177RP
The change in entropy of helium is
Explanation of Solution
Write the expression for the ideal gas equation to calculate the mass of helium.
Here, mass of helium is m, initial pressure is
Write the expression to calculate the change in entropy of helium.
Here, mass of helium is m, specific heat at constant pressure is
Conclusion:
From Table A-1E, “the molar mass, gas constant and critical–point properties table”, select the gas constant of helium as
Substitute
From Table A-2E, “Ideal-gas specific heats of various common gases”, select the specific heat at constant pressure
Substitute
Thus, the change in entropy of helium is
b)
The entropy change of the surrounding.
Answer to Problem 177RP
The entropy change of the surrounding is
Explanation of Solution
Write the expression to calculate the ideal gas equation for initial and final condition.
Here, final volume is
Write the expression for the polytropic process.
Rewrite the Equation (IV) to calculate exponent n.
Write the expression to calculate the boundary work for the polytropic process
Write the expression for the energy balance equation of the system.
Here, net energy transfer inside the system is
Write the expression to calculate the entropy change of the surrounding.
Here, surroundin temperature is
Conclusion:
Substitute
Substitute
Substitute
Substitute
Here, heat transfer output is
Substitute
Here, the entropy change of the surrounding is
Substitute
Thus, the entropy change of the surrounding is
c)
Whether this process is reversible, irreversible, or impossible.
Answer to Problem 177RP
The total entropy change during the process is
The system is irreversible.
Explanation of Solution
Write the expression to calculate the total entropy change during the process.
Here, the total entropy change in the system is
Conclusion:
Substitute
Thus, the total entropy change during the process is
The obtained value of the total entropy change
Thus, the system is irreversible.
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Chapter 7 Solutions
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