Thermodynamics - Saturated Vapor Quality Question

In summary: What is your source for this specific volume number?In summary, the quality of the saturated vapor in the 4 cubic meter rigid vessel containing 0.04 cubic meters of liquid water and 3.96 cubic meters of water vapor at 101.325 kPa is 0.05818. This was calculated by dividing the mass of the vapor (2.367 kg) by the total mass (40.681 kg).
  • #1
MechE2015
19
0

Homework Statement



A 4 cubic meter rigid vessel contains 0.04 cubic meters of liquid water and 3.96 cubic meters of water vapor at 101.325 kPa. What is the quality of the saturated vapor?

Homework Equations



Specific volume of saturated liquid at 100 C and 101.325 kPa: 0.001044 m^3/kg
Specific volume of saturated vapor at 100 C and 101.325 kPa: 1.67290 m^/kg
Mass of Vapor = (Volume vapor) / (Specific Volume of sat. vapor)
Mass of water = (Volume water) / (Specific Volume of sat. liquid)
x = (Mass of Vapor) / (Total Mass)


The Attempt at a Solution



Mass of liquid: 0.04/0.001044 = 38.314 kg
Mass of vapor: 3.96/1.67290 = 2.367 kg

x = 2.367/(38.314+2.367) = 0.05818

Also, for some reason, I thought the quality could be found by specific volumes, which would give me: x = (1.5313-0.001044)/(1.6729) = 0.9147

Could anyone tell me which method is correct? We have used specific volume to find the quality a few times, which confuses me as to why this would be different.
 
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  • #2
MechE2015 said:

Homework Statement



A 4 cubic meter rigid vessel contains 0.04 cubic meters of liquid water and 3.96 cubic meters of water vapor at 101.325 kPa. What is the quality of the saturated vapor?

Homework Equations



Specific volume of saturated liquid at 100 C and 101.325 kPa: 0.001044 m^3/kg
Specific volume of saturated vapor at 100 C and 101.325 kPa: 1.67290 m^/kg
Mass of Vapor = (Volume vapor) / (Specific Volume of sat. vapor)
Mass of water = (Volume water) / (Specific Volume of sat. liquid)
x = (Mass of Vapor) / (Total Mass)

The Attempt at a Solution



Mass of liquid: 0.04/0.001044 = 38.314 kg
Mass of vapor: 3.96/1.67290 = 2.367 kg

x = 2.367/(38.314+2.367) = 0.05818
That looks right to me. :approve: (ignoring any trivial rounding differences, if any)
Also, for some reason, I thought the quality could be found by specific volumes, which would give me: x = (1.5313-0.001044)/(1.6729) = 0.9147
Forgive me, but I have no idea what you're doing there. You'll have to explain your reasoning.
 
  • #3
@collinsmark

I think I had an error computing the specific volume, and if I correct it with the specific volume of 0.09833 m^3/kg, the I get a quality = (0.09833 - 0.001044) / (1.6729 - 0.001044) = 0.05818

Sorry for the confusion but I think I found my mistake with the incorrect computation for specific volume.
 
  • #4
MechE2015 said:
@collinsmark

I think I had an error computing the specific volume, and if I correct it with the specific volume of 0.09833 m^3/kg, the I get a quality = (0.09833 - 0.001044) / (1.6729 - 0.001044) = 0.05818

Sorry for the confusion but I think I found my mistake with the incorrect computation for specific volume.
Okay. But where does the the 0.09833 m3/kg come from? It's the specific volume of what exactly? Again, forgive me, but I'm just not following.
 
  • #5


I would like to clarify that both methods are correct, but they are used for different scenarios. The first method, using the mass of the liquid and vapor, is used when the total mass of the system is known. In this case, we can find the quality by dividing the mass of the vapor by the total mass of the system.

The second method, using specific volumes, is used when the total volume of the system is known. In this case, we can find the quality by calculating the difference between the specific volumes of the vapor and liquid, and then dividing it by the specific volume of the vapor.

It is important to understand the difference between these two methods and when to use them in order to accurately find the quality of the saturated vapor. It is also important to note that the specific volumes of the vapor and liquid may vary depending on the temperature and pressure, so it is important to use the correct values for the specific scenario given.
 

FAQ: Thermodynamics - Saturated Vapor Quality Question

1. What is saturated vapor quality?

Saturated vapor quality, also known as dryness fraction, is a thermodynamic property that describes the ratio of the mass of vapor to the total mass of a two-phase mixture at a given pressure and temperature.

2. How is saturated vapor quality calculated?

Saturated vapor quality can be calculated by dividing the mass of vapor in a mixture by the total mass of the mixture. This can be determined using a steam table or by using the equation x = (m - mf) / (mg - mf), where x is the saturated vapor quality, m is the actual mass of the mixture, mf is the mass of the liquid phase, and mg is the mass of the vapor phase.

3. What is the significance of saturated vapor quality in thermodynamics?

The saturated vapor quality is an important parameter in thermodynamics as it helps determine the state of a two-phase mixture and its properties. It is also used in the analysis of vapor compression refrigeration cycles and power cycles.

4. How does saturated vapor quality affect the behavior of a substance?

The saturated vapor quality affects the behavior of a substance by indicating the amount of vapor present in a two-phase mixture. It also influences the thermodynamic properties of the mixture, such as enthalpy, entropy, and specific volume.

5. What is the difference between saturated vapor quality and degree of superheat?

Saturated vapor quality and degree of superheat are both thermodynamic properties that describe the state of a substance. However, saturated vapor quality refers to the ratio of vapor to the total mixture, while degree of superheat refers to the difference between the actual temperature and the saturation temperature at a given pressure.

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