A well-insulated rigid tank contains 6 lbm of a saturated liquid–vapor mixture of water at 35 psia. Initially, three-quarters of the mass is in the liquid phase. An electric resistance heater placed in the tank is turned on and kept on until all the liquid in the tank is vaporized. Assuming the surroundings to be at 75°F and 14.7 psia, determine (a) the exergy destruction and (b) the second-law efficiency for this process.
(a)
The exergy destruction.
Answer to Problem 33P
The exergy destruction is
Explanation of Solution
Express the entropy balance for the two constant pressure devices.
Here, net entropy transfer by heat and mass is
Substitute
Express the exergy destruction.
Here, surrounding temperature is
Here, final specific volume is
Express initial specific volume.
Here, initial quality is
Express initial specific internal energy.
Here, specific internal energy at saturated liquid and evaporation is
Express initial specific entropy.
Here, specific entropy at saturated liquid and evaporation is
Conclusion:
Express initial quality.
Refer Table A-5E, “saturated water-pressure table” and write the properties corresponding to initial pressure
Substitute
Substitute
Substitute
As the specific volumes are constant, take initial and final specific volume as equal.
Here, specific final volume is
Refer Table A-5E, “saturated water-pressure table”, obtain the below properties at specific volume at saturated vapor of
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y are specific volume at saturated vapor and specific internal energy at saturated vapor respectively.
Show final specific internal energy at specific volume of
Saturated vapor, | |
3.2202 | 1109.9 |
2.9880 | |
3.0150 | 1110.8 |
Express final specific internal energy using interpolation method.
Substitute
From above calculation the final specific internal energy is
Refer Table A-5E, “saturated water-pressure table”, obtain the below properties at specific volume at saturated vapor of
Show final specific entropy at specific volume of
Saturated vapor, | |
3.2202 | 1.5757 |
2.9880 | |
3.0150 | 1.5700 |
Substitute
From above calculation the final specific entropy is
Substitute
Substitute
Hence, the exergy destruction is
(b)
The second law efficiency for the process.
Answer to Problem 33P
The second law efficiency for the process is
Explanation of Solution
Write the expression for the energy balance equation.
Here, the total energy entering the system is
Express the reversible work during process.
Express the second law efficiency for the process.
Conclusion:
Substitute
Substitute
Substitute
Hence, the second law efficiency for the process is
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Chapter 8 Solutions
Thermodynamics: An Engineering Approach
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