Example Problem with Complete Solution

2D-1 : Isothermal Vaporization of Water 4 pts
A piston-and-cylinder device contains 25 lbm of water at 195oF. The cylinder rests in a constant temperature bath that keeps the temperature of the water in the cylinder at 195oF.
Weights are removed one at a time from the back of the piston causing the pressure inside the cylinder to drop from a very high value until the water inside begins to boil.
Eventually, the last drop of water in the cylinder vaporizes. Determine the total volume of the steam in the cylinder at this point, in ft3.

Read : The initial state of the water is probably a subcooled liquid (or even a supercritical fluid), since the pressure is "very high".  The final state of the water is a saturated vapor because the vaporization of the water is just barely complete.  The temperature of the final saturated vapor is the same as the initial temperature: 205oF.  This is an isothermal process !
Given: m 25 lbm T 195 oF
Find: Vfinal ??? ft3
Assumptions: 1- The initial and final states are equilibrium states.
2- In the initial state, the system contains subcooled liquid water.
3- In the final state, the system contains saturated water vapor.
xfinal 1 lbm vap/lbm
Equations / Data / Solve:
We need to determine the volume of the system and we are given the mass of water in the system.
We need to determine the specific volume of the system because :
Eqn 1
Because we know that the water in the final state is a saturated vapor, we can look up its specific volume in the Saturated Temperature Table of the Steam Tables at 195oF.
The problem is that a temperature of 195oF is not listed in the Saturation Temperature Table.
So, we must interpolate to determine the value : Tsat Vsat vap
(oF) (ft3/lbm)
190 40.916
195 ???
200 33.609
Eqn 2
Eqn 3
slope -0.73071 (ft3/lbm)/oF Vsat vap 37.263 ft3/lbm
Now that we know the value of the specific volume of the saturated vapor, and the system contains ALL saturated vapor (x = 1), we can plug values into Eqn 1 and answer the question.
Vfinal 931.6 ft3
Verify: None of these assumptions can be verified.
Answers : Vfinal 932 ft3