
The work and heat transfer for each process.

Answer to Problem 176RP
The heat transfer for the isothermal process 1–2 is
The work done during the process 1-2 is
The work done during the isentropic compression process 2-3 is
The heat transfer for the isentropic process 2–3 is
The work done during constant pressure compression process 3-1 is
The heat transfer during constant pressure compression process 3-1 is
Explanation of Solution
Write the expression to calculate the enthalpy change in process 1-2.
Here, pressure at process 1 is
Write the expression to calculate the ideal gas equation, to find mass of the air.
Here, mass of the air is m , volume at process 1 is
Write the expression to calculate the heat transfer for the isothermal process 1–2.
Here, enthalpy change in process 1-2 is
Write the expression to calculate the work done during the process 1-2
Write the expression to calculate the work done during the isentropic compression process 2-3
Here, mass of the air is m, internal energy at process 3 is
Write the expression to calculate the relative pressure at process 3
Here, relative pressure at process 2 is
Write the expression to calculate the volume at process 3
Write the expression to calculate the work done during constant pressure compression process 3-1
Here, volume at process 3 is
Write the expression to calculate the heat transfer during constant pressure compression process 3-1
Here, heat transfer during constant pressure compression process 3-1 is
Conclusion:
From Table A-1 “the molar mass, gas constant and critical point properties table”, obtain the gas constant
Substitute
Substitute 1.394 kg for m,
Substitute
Thus, the heat transfer for the isothermal process 1–2 is
Substitute
Thus, the work done during the process 1-2 is
From Table A-17, “Ideal-gas properties of air”, obtain the internal energy
Substitute
Refer to Table A-17, “Ideal-gas properties of air”.
Obtain the select the internal energy
Write the formula of interpolation method of two variables.
Here, the variables denoted by x and y are relative pressure and internal energy.
Show relative pressure and internal energy values from the Table A-17.
Relative pressure | Internal energy |
3.481 | 278.93 |
3.696 | ? |
3.806 | 286.16 |
Substitute
The value of internal energy process 1
Show temperature and initial internal energy values from the Table A-17.
Temperature | Internal energy |
3.481 | 390 |
3.696 | ? |
3.806 | 400 |
Substitute
The value of Temperature
Substitute 1.394 kg for m,
Thus, the work done during the isentropic compression process 2-3 is
The heat transfer for the isentropic process 2–3 is zero when entropy change remains unchanged for the isentropic compression process.
Thus, the heat transfer for the isentropic process 2–3 is
Substitute 1.394 kg for m,
Substitute
Thus, the work done during constant pressure compression process 3-1 is
Substitute 37 kJ for
Thus, the heat transfer during constant pressure compression process 3-1 is
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Chapter 7 Solutions
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