| 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. |
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| 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 ! |
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25 |
lbm |
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T |
195 |
oF |
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| Find: |
Vfinal |
??? |
ft3 |
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| Assumptions: |
1- The initial and
final states are equilibrium states. |
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2- In the initial
state, the system contains subcooled liquid water. |
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3- In the final state,
the system contains saturated water vapor. |
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xfinal |
1 |
lbm vap/lbm |
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| Equations
/ Data / Solve: |
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We need to determine
the volume of the system and we are given the mass of water in the system. |
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We need to determine
the specific volume of the system because : |
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Eqn 1 |
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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. |
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The problem is that a
temperature of 195oF is not listed in the Saturation Temperature Table. |
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So, we must
interpolate to determine the value : |
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Tsat |
Vsat vap |
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(oF) |
(ft3/lbm) |
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190 |
40.916 |
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195 |
??? |
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200 |
33.609 |
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Eqn 2 |
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Eqn 3 |
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slope |
-0.73071 |
(ft3/lbm)/oF |
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Vsat vap |
37.263 |
ft3/lbm |
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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. |
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Vfinal |
931.6 |
ft3 |
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| Verify: |
None of these assumptions
can be verified. |
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| Answers : |
Vfinal |
932 |
ft3 |
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