2C-2 : | State of a System at a Given Temperature and Pressure | 4 pts |
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Ammonia
exists in a sealed tank at each of the following temperatures and pressures. In each case, what phase or phases
could exist in the system? Show
your work and explain your reasoning. |
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a.) 25^{o}C, 114.7 kPab.) -31.59 ^{o}C, 50
kPac.) -18.85 ^{o}C, 200
kPad.) -37.41 ^{o}C, 100
kPa |
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Read : | At these temperatures
and pressures, it is safe to assume that no solid water, or ice, exists in
the system. So, the question becomes
whether the system contains superheated vapor or subcooled liquid or whether
the system is in VLE. If the system is
in VLE, then P = P*(T). Another way to look at this is that T = T_{sat}(P). At saturation, it is not possible to
determine the quality of the system without knowing the value of another
intensive variable, such as v, u or h.
So, we are not able to state whether both vapor and liquid exist, but
we can say that both could exist under these conditions. Fortunately, that is exactly what we are
asked to determine in this problem. |
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Given: | Part a.) | T | 25 | ^{o}C |
P | 114.7 | kPa | |||||||

Part b.) | T | -31.59 | ^{o}C |
P | 50 | kPa | ||||||||

Part c.) | T | -18.85 | ^{o}C |
P | 200 | kPa | ||||||||

Part d.) | T | -37.41 | ^{o}C |
P | 100 | kPa | ||||||||

^{} |
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Find: | What phase or phases could exist in the system? | Explain. | ||||||||||||

Assumptions: | 1- No solid water, or ice, exists in the system. | |||||||||||||

Equations / Data / Solve: | ||||||||||||||

In each part of this problem, we need to determine the saturation temperature associated with the system pressure. Then we can compare the actual system temperature to the saturation temperature. | ||||||||||||||

If : | T_{sys}
> T_{sat} |
Then : | The system contains a superheated vapor. | |||||||||||

If : | T_{sys}
< T_{sat} |
Then : | The system contains a subcooled liquid. | |||||||||||

If : | T_{sys}
= T_{sat} |
Then : | The system could contain an equilibrium mixture of saturated liquid and saturated vapor. | |||||||||||

This is not always the easiest approach and for this part of the problem, there is an easier approach. | ||||||||||||||

Another way to solve
this problem is to determine the vapor pressure of water at the actual system
temperature. We can then compare the
actual system pressure to the vapor pressure at T_{sys}. |
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If : | P_{sys} < P*(T_{sys}) |
Then : | The system contains a superheated vapor. | |||||||||||

If : | P_{sys} > P*(T_{sys}) |
Then : | The system contains a subcooled liquid. | |||||||||||

If : | P_{sys} = P*(T_{sys}) |
Then : | The system could contain an equilibrium mixture of saturated liquid and saturated vapor. | |||||||||||

Part a.) | The second
method is easier for part (a)
because T_{sys} = 25^{o}C is listed in the Saturated Temperature Table while P_{sys} = 114.7 kPa is not listed in the Saturation
Pressure Table.
So, let's use the 2nd method ! |
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From the Saturation Temperature Table of the Ammonia Tables : | P*(25^{o}C) |
1003.2 | kPa | |||||||||||

Since P_{sys} < P*(T_{sys}), we conclude : |
The system contains superheated ammonia vapor. | |||||||||||||

Part b.) | In this part of the
problem, it is easier to use method 1, described in part
(a), because P_{sys} appears in the
saturation tables, while T_{sys} does not. |
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From the Saturation Pressure Table of the Ammonia Tables : | T_{sat}(50 kPa) |
-46.52 | ^{o}C |
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Since T_{sys} > T_{sat}(P_{sys}), we conclude : |
The system contains superheated ammonia vapor. | |||||||||||||

Part c.) | In this part of the
problem, it is easier to use method 1, described in part
(a), because P_{sys} appears in the
saturation tables, while T_{sys} does not. |
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From the Saturation Pressure Table of the Steam Tables : | T_{sat}(200
kPa) |
-18.85 | ^{o}C |
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Since
T_{sys} = T_{sat}(P_{sys}), we conclude : |
The system could contain an equilibrium mixture of saturated liquid and saturated vapor. | |||||||||||||

^{} |
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Part d.) | In this part of the
problem, it is easier to use method 1, described in part a, because P_{sys} appears in the saturation tables, while T_{sys} does not. |
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From the Saturation Pressure Table of the Ammonia Tables : | T_{sat}(100 kPa) |
-33.59 | ^{o}C |
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Since T_{sys} < T_{sat}(P_{sys}), we conclude : |
The system contains subcooled liquid ammonia. | |||||||||||||

^{} |
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Verify: | Since all of the temperature and pressure combination in this problm appear in the ammonia tables for vapor-liquid equilibrium, no solid ammonia, or ammonia ice, is present in any of the four systems considered. | |||||||||||||

Answers : | Part a.) | Superheated vapor. | Part c.) | Saturated mixture. | ||||||||||

Part b.) | Superheated vapor. | Part d.) | Subcooled liquid. |