| 2B-1 : | Condensing Water Vapor by Increasing the Pressure | 3 pts |
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| A piston-and-cylinder device contains water vapor at 135oC and 1 atm in state 1. The cylinder contains no air and no liquid water. The cylinder is surrounded by a water bath at 135oC that keeps the temperature of the | ||||||||||||||||||||
| contents of the cylinder constant. The piston is pushed slowly downward causing the pressure to increase steadily. Eventually, a
small droplet of liquid water forms in state 2. |
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| a.) Describe the state of the contents of the cylinder in state 1 and in state 2. |
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| b.) Sketch the path of this process on a PV Diagram. Be sure to label all the regions on the diagram and include the two-phase envelope and all relevant isotherms. | ||||||||||||||||||||
| Read : | The keys to this
problem are… 1- The process is isothermal because the constant temperature bath keeps the system at 135oC and 2- The final state is saturated vapor because the 1st micro-droplet of lquid water condenses. |
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| Given: | T1 | 135 | oC | T2 | 135 | oC | ||||||||||||||
| P1 | 1 | atm | P2 > P1 | |||||||||||||||||
| x2 | 1 | kg vap/kg | ||||||||||||||||||
| Find: | a.) | Describe states 1 & 2 | ||||||||||||||||||
| b.) | Sketch process path on a PV Diagram | |||||||||||||||||||
| Assumptions: | 1- The constant temperature bath is prefectly effective in keeping the contents of the cylinder at a constant and uniform temperature of 135oC. | |||||||||||||||||||
| Equations / Data / Solve: | ||||||||||||||||||||
| Part a.) | - In state 1, the cylinder contains all water vapor. - The pressure must be increased on this vapor in order to cause any liquid water droplets to condense. - We can conclude that P1 = 1 atm is lower than the vapor pressure (or saturation pressure) of water at T1 = 135oC. - Therefore the water vapor in state 1 is a superheated vapor. |
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| - In state 1, the cylinder contains all water vapor. - The pressure on this vapor is just exactly high enough to cause a micro-droplet of liquid water to condense. - We can conclude that P2 = P*(135oC), the vapor pressure (or saturation pressure) of water at T1 = 135oC. - Therefore the water vapor in state 1 is a saturated vapor. |
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| Part b.) | 
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| Verify: | This assumption cannot be veriefied without experimentation. | |||||||||||||||||||
| Answers : | See above. | |||||||||||||||||||
