How to find specific volume given temperature?

In summary, the conversation discusses the process of finding specific volume for a given temperature and pressure using tables. The pressure is found to be in the superheated phase, but the value is not available in the tables. Interpolation is suggested, with an emphasis on interpolating on Pv rather than simply on v for better accuracy. The process for finding specific volume for sub-cooled liquid is also discussed, and it is advised to use Pv for interpolation. An example of interpolation is given, and a mistake is corrected.
  • #1
EastWindBreaks
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3

Homework Statement



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Homework Equations


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The Attempt at a Solution


upload_2017-12-8_6-47-59.png

I don't understand how the solution got its values, not from the tables right? because I couldn't find such value from all of the tables. Since the pressure is less than the saturated pressure at given temperature, it is in super heated phase. but 90.4 kpa equals 13.1 psia, which is not in the super heated table. can we calculate specific volume without the tables? can we find its volume by finding the density at given temperature and pressure since the mass is known? but which would also require a table to find such density...
 

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  • #2
Your book (Moran et al) also has a table in metric units, doesn't it?
 
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  • #4

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  • #5
EastWindBreaks said:
Thank you, I found the SI system tables, but i still don't see 0.2302, it is in this region correct? View attachment 216340
where P= 0.10 MPa
Yes. You have to interpolate in the table. Since the behavior is close to ideal gas behavior (with Pv nearly constant), for good accuracy, you should interpolate on (Pv) rather than simply on v.
 
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  • #6
Chestermiller said:
Yes. You have to interpolate in the table. Since the behavior is close to ideal gas behavior (with Pv nearly constant), for good accuracy, you should interpolate on (Pv) rather than simply on v.
BvU said:

got it, so we have to do linear interpolate (assume the trend is linear?) for vapors when the table doesn't have the value we want, and we use quality(
upload_2017-12-10_21-46-25.png
)to find the properties for saturated state where the temperature and pressure are dependent on each other. Do we use
upload_2017-12-10_21-46-51.png
to find properties of sub cooled liquid as well? since I did not find a table for sub-cooled liquid.
 

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  • #7
EastWindBreaks said:
got it, so we have to do linear interpolate (assume the trend is linear?) for vapors when the table doesn't have the value we want, and we use quality(View attachment 216469 )to find the properties for saturated state where the temperature and pressure are dependent on each other. Do we use View attachment 216470 to find properties of sub cooled liquid as well? since I did not find a table for sub-cooled liquid.
You should be able to find the tabulated values of sub cooled liquid in your tables (sometimes called pressurized liquids).

I also point out again that, unless you interpolate on Pv rather than v, you will not get an accurate answer for the interpolated v. I guarantee that you linear interpolation will not deliver 0.2303.
 
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  • #8
Chestermiller said:
You should be able to find the tabulated values of sub cooled liquid in your tables (sometimes called pressurized liquids).

I also point out again that, unless you interpolate on Pv rather than v, you will not get an accurate answer for the interpolated v. I guarantee that you linear interpolation will not deliver 0.2303.

Thank you, now I understand what you said about Pv being nearly constant. I just want to confirm, you said interpolate on Pv, you mean like this?:
upload_2017-12-11_0-59-35.png

I got v= 0.2326, a little off from 0.2302.
 

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  • #9
At P= 60000 Pa, v = 0.35048 m^3/kg, and Pv = 21029 J/kg

At P = 100000 Pa, v = 0.20743 m^3/kg, and Pv = 20743 J/kg

So, at P = 90400 Pa, $$Pv=21029+\frac{(90400-60000)}{(100000-60000}(20743-21029)=20812$$ And, ##v=20812/90400=0.2302## m^3/kg.
 
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  • #10
Chestermiller said:
At P= 60000 Pa, v = 0.35048 m^3/kg, and Pv = 21029 J/kg

At P = 100000 Pa, v = 0.20743 m^3/kg, and Pv = 20743 J/kg

So, at P = 90400 Pa, $$Pv=21029+\frac{(90400-60000)}{(100000-60000}(20743-21029)=20812$$ And, ##v=20812/90400=0.2302## m^3/kg.

Thanks a lot! I am so careless, I made a mistake by using P2= 0.14 Mpa instead of 0.1 Mpa.
 

Related to How to find specific volume given temperature?

What is specific volume and why is it important?

Specific volume is the volume occupied by one unit of mass of a substance. It is important because it helps determine the density of a substance and its relationship with other thermodynamic properties.

What is the formula for calculating specific volume?

The formula for calculating specific volume is v = V/m, where v is specific volume, V is volume, and m is mass.

How does temperature affect specific volume?

Temperature has a direct relationship with specific volume. As temperature increases, specific volume also increases. This is because as temperature increases, the kinetic energy of molecules increases, causing them to take up more space and therefore increase in volume.

What are some common units for specific volume?

Some common units for specific volume include cubic meters per kilogram (m^3/kg), cubic centimeters per gram (cm^3/g), and liters per kilogram (L/kg).

Can specific volume be negative?

No, specific volume cannot be negative. It is a physical property that represents the amount of space occupied by a substance, which cannot be negative.

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