# How to find the specific volume?

1. Jan 10, 2013

### xCuzIcanx

1. The problem statement, all variables and given/known data

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.

2. Jan 10, 2013

### haruspex

You can't even quote some relevant equations?

3. Jan 10, 2013

### xCuzIcanx

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.

4. Jan 10, 2013

### Staff: Mentor

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

5. Jan 10, 2013

### xCuzIcanx

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?

6. Jan 10, 2013

### Staff: Mentor

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

$v = \frac{V}{nm}$ 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).

7. Jan 10, 2013

### xCuzIcanx

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

8. Jan 10, 2013

### Staff: Mentor

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).