Example Problem with Complete Solution

2B-1 : Condensing Water Vapor by Increasing the Pressure 3 pts
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.
a.) Describe the state of the contents of the cylinder in state 1 and in state 2.
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.
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.
- 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.
Part b.)
Verify: This assumption cannot be veriefied without experimentation.
Answers : See above.