Concept explainers
A piston–cylinder device contains 0.15 kg of air initially at 2 MPa and 350°C. The air is first expanded isothermally to 500 kPa, then compressed polytropically with a polytropic exponent of 1.2 to the initial pressure, and finally compressed at the constant pressure to the initial state. Determine the boundary work for each process and the net work of the cycle.
The boundary work for the isothermal expansion process of a piston-cylinder device.
The boundary work for the polytropic compression process of a piston-cylinder device.
The boundary work for the constant pressure compression process of a piston-cylinder device.
The net-work for cycle is the sum of the works for each process of a piston-cylinder device.
Answer to Problem 20P
The boundary work for the isothermal expansion process of a piston-cylinder device is
The boundary work for the polytropic compression process of a piston-cylinder device is
The boundary work for the constant pressure compression process of a piston-cylinder device is
The net-work for cycle is the sum of the works for each process of a piston-cylinder device is
Explanation of Solution
Show the free body diagram of the piston-cylinder device contains air.
Determine the process 1 volume of an ideal gas.
Here, the mass of a piston-cylinder device is
Determine the process 2 volume of an ideal gas.
Here, the mass of a piston-cylinder device is
Write the expression for the boundary work for isothermal expansion process (1-2) of an ideal gas.
Determine an ideal gas for polytropic compression process.
Here, the process 3 pressure of a piston-cylinder device is
Write the expression for the boundary work for polytropic compression process of an ideal gas.
Write the expression for the boundary work for constant pressure compression process of an ideal gas.
Determine the net-work for cycle is the sum of the works for each process of a piston-cylinder device.
Conclusion:
From the Table 4-2a, “Ideal-gas specific heat of various common gases”, obtain the value gas constant for air as
Substitute
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Thus, the boundary work for the isothermal expansion process of a piston-cylinder device is
Substitute
Substitute
Thus, the boundary work for the polytropic compression process of a piston-cylinder device is
Substitute
Thus, the boundary work for the constant pressure compression process of a piston-cylinder device is
Substitute
Thus, the net-work for cycle is the sum of the works for each process of a piston-cylinder device is
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Chapter 4 Solutions
THERMODYNAMICS: AN ENGINEERING APPROACH
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