A pistonandcylinder device contains 25 lb_{m} of water at 195^{o}F. The cylinder rests in a constant temperature
bath that keeps the temperature of the water in the cylinder at 195^{o}F. 
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 ft^{3}. 


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: 205^{o}F. This is an isothermal
process ! 










Given: 
m 
25 
lb_{m} 



T 
195 
^{o}F 










Find: 
V_{final} 
??? 
ft^{3} 
















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. 














x_{final} 
1 
lb_{m} vap/lb_{m} 














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 195^{o}F. 











The problem is that a
temperature of 195^{o}F is not listed in the Saturation Temperature Table. 











So, we must
interpolate to determine the value : 

T_{sat} 
V_{sat vap} 








(^{o}F) 
(ft^{3}/lb_{m}) 








190 
40.916 








195 
??? 








200 
33.609 

















Eqn 2 

















Eqn 3 











slope 
0.73071 
(ft^{3}/lb_{m})/^{o}F 



V_{sat vap} 
37.263 
ft^{3}/lb_{m} 











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. 

















V_{final} 
931.6 
ft^{3} 










Verify: 
None of these assumptions
can be verified. 















Answers : 
V_{final} 
932 
ft^{3} 















