How to find the specific volume?

[xCuzIcanx]

Homework Statement

So a chart is given.
| | Water vapor at p (pressure)=0.006MPa | Water vapor at p (pressure)=0.035
| T(in degree C) | v(m^3/kg) | v(m^3/kg)
| 80 | 27.132 | 4.526
| 120 | 30.219 | 4.625

Find: Specific v (m3/kg) at T = 100 oC and p = 0.01 MPa Show work

I don't even know where to begin.

 

[haruspex]

You can't even quote some relevant equations?

 

[xCuzIcanx]

You can't even quote some relevant equations?

Well a new semester started and the teacher didn't give us anything except to do this problem.. I wish I knew what was going on but the teacher only taught us definitions and nothing else.

 

[Chestermiller]

What is the equation for the specific volume of a gas as a function of temperature, pressure, molecular weight, and gas constant predicted by the ideal gas law. If you apply this equation to water vapor at the three sets of conditions in this problem, what does the ideal gas law predict for the specific volume in each case?

Chet

 

[xCuzIcanx]

What is the equation for the specific volume of a gas as a function of temperature, pressure, molecular weight, and gas constant predicted by the ideal gas law. If you apply this equation to water vapor at the three sets of conditions in this problem, what does the ideal gas law predict for the specific volume in each case?

Chet

I know that the ideal gas law equation is PV=nRT

and so then would the relevant equation be v=V/m? which is v=RT/P?

 

[Chestermiller]

I know that the ideal gas law equation is PV=nRT

and so then would the relevant equation be v=V/m? which is v=RT/P?

No, but you are close. The correct result is:

[itex]v = \frac{V}{nm}[/itex] in volume per unit mass units,

where m is the molecular weight. Now substitute into the ideal gas law. Then calculate the specific volume of water in the three cases as if it were an ideal gas. Make a table with two columns: column 1 is the specific volume calculated from the ideal gas law; column 2 is the observed specific volume (there will be a blank in the table for the observed specific volume that you are solving for).

 

[xCuzIcanx]

Oh all right, but can you do this with double interpolation? if so what would be the process

 

[Chestermiller]

Oh all right, but can you do this with double interpolation? if so what would be the process

If wouldn't be a double interpolation. It would only be a single interpolation: predicted specific volume versus observed specific volume. It is not possible with this information to get the exact right result. You are just using your fundamental knowledge base to make your best estimate. Even with this, it is going to have to be a linear interpolation. You might also try to do this problem using the compressibility factor z and the corresponding states plot (if you have learned about that yet).