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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)
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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)
![Check Mark](/static/check-mark.png)
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)
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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
Loose Leaf for Thermodynamics: An Engineering Approach
- Steam enters an adiabatic turbine steadily at 7 MPa, 500°C, and 45 m/s and leaves at 100 kPa and 75 m/s. If the power output of the turbine is 5 MW and the isentropic efficiency is 77 percent, determine the mass flow rate of steam through the turbine.arrow_forwardSteam enters an adiabatic turbine steadily at 7 MPa, 500°C, and 45 m/s and leaves at 100 kPa and 75 m/s. If the power output of the turbine is 5 MW and the isentropic efficiency is 77 percent, determine the rate of entropy generation during this process.arrow_forwardAn adiabatic diffuser at the inlet of a jet engine increases the pressure of the air that enters the diffuser at 11 psia and 30°F to 20 psia. What will the air velocity at the diffuser exit be if the diffuser isentropic efficiency, defined as the ratio of the actual kinetic energy change to the isentropic kinetic energy change, is 82 percent and the diffuser inlet velocity is 1200 ft/s?arrow_forward
- If you know that the change in entropy of a system where heat was added is 12 J/K, and that the temperature of the system is 250 K, what is the amount of heat added to the system?arrow_forwardtwo aluminum ingots, one weighing 1.5 kg at 450 degrees celsius while the other is 1.1 kg at 250 degrees celsius, are placed in an insulated enclosure. assuming there is no heat transfer from the ingots to the enclosure material, determine the final temperature and the entropy associated with the process.arrow_forwardA piston is inserted into a cylinder causing the pressure in the air to change from 50 to 4000 kPa while the temperature remains constant at 27°C. To accomplish this, heat transfer must occur. Determine the entropy change.arrow_forward
- Refrigerant-134a at 140 kPa and –10°C is compressed by an adiabatic 0.5-kW compressor to an exit state of 700 kPa and 60°C. Neglecting the changes in kinetic and potential energies and assuming the surroundings to be at 27°C, determine the second-law efficiency of the compressor.arrow_forwardA piston–cylinder device contains superheated steam. During an actual adiabatic process, the entropy of the steam will (never, sometimes, always) increasearrow_forwardA mass of 25 lbm of helium undergoes a process from an initial state of 50 ft3 /lbm and 60°F to a final state of 20 ft3 /lbm and 240°F. Determine the entropy change of helium during this process, assuming the process is reversible.arrow_forward
- Steam enters an adiabatic turbine at 5 MPa, 650C, and 80 m/s and leaves at 50 kPa, 1508C, and 140 m/s. If the power output of the turbine is 8 MW, determine (a) the mass flow rate of the steam flowing through the turbine and (b) the isentropic efficiency of the turbine.arrow_forwardWater vapor enters a turbine at 6 MPa and 400C, and leaves the turbine at 100 kPa with the same specific entropy as that at the inlet. Calculate the difference between the specific enthalpy of the water at the turbine inlet and exit.arrow_forwardAssuming that the composite system is closed and isolated, what is the minimum increase in the entropy of substance 2 in order for this process to occur?arrow_forward
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