Thermodynamics - Pure substance problem

[Xyius]

Hey everyone, I am doing a problem and I am on the "Properties of Pure substances" chapter of the book. These problems basically involve going to lookup tables and reading the values to use in the problem, so I am hoping I can still get some help even though you might not have the thermodynamic tables to look up. :\

Homework Statement

A spring loaded piston-cylinder device is initially filled with 0.2 lbm of an R-134a liquid-vapor mixture whose temperature is -30 degrees Fahrenheit and whose quality is 80%. The spring constant in the spring force relation F=ks is 37 lbf/in, and the piston diameter is 12 inches. The R-134a undergoes a process that increases its volume by 40%. Calculate the final temperature and enthalpy of the R-134a.

Homework Equations

$$Quality=x=\frac{m_{vapor}}{m_{total}}$$
$$v_{avg}=v_{f}+xv_{fg}$$

$$m=mass$$
$$v=specific volume$$
$$v_{g}=Specific volume of the gas$$
$$v_{f}=Specific volume of the fluid$$
$$v_{fg}=v_{g}-v_{f}$$

The Attempt at a Solution

Since I am not given the mass of the piston I am assuming I can ignore the weight of it. (I do not know if this is valid or not.) Summing the forces in the y direction I get...

$$\sum F_{y}=0=ks-PA$$

$$ks=PA$$
$$s=\frac{PA}{k}=\frac{9.869(\pi (0.5^2))}{37(12)}=0.017ft$$
NOTE: I had to go to the thermodynamic tables and look under -30 degrees F in "Saturated R-134a" to obtain the saturation pressure of 9.869 psia. I also converted 37 lbf/in to lbf/ft and the 6 inch radius to 0.5 ft.

I do not know what this represents though, or if it helps at all with the problem. I am guessing that this is the distance from the springs equilibrium point.

Another thing I can do is find the mass of the gas and liquid using the definition of quality (x). I get 0.16lbm for the gas and 0.04lbm for the liquid. Again, not sure what good this does me either.

Somehow I believe I need to get to the specific volume of state 2 after it has expanded 40%, and then look this value up in the tables.

Any help would GREATLY be appreciated.

 

[jbsteele]

Thanks. A:You are on the right track. You have already calculated the displacement of the piston from the force equilibrium equation, so you know how much the volume has increased. You can use this to calculate the final specific volume $v_2$ for the R-134a by $$v_2 = v_1 \left( \frac{V_2}{V_1} \right)$$where $v_1$ is the initial specific volume and $V_2/V_1$ is the ratio of the final to initial volumes. You can use the quality x to calculate the initial specific volume of the R-134a as $$v_1=v_f + x v_{fg}$$where $v_f$ and $v_{fg}$ are the specific volumes of saturated liquid and saturated vapor respectively at the initial temperature. Now you have the specific volume $v_2$ and the initial temperature of the R-134a -30°F. You can use the thermodynamic tables to look up the enthalpy and temperature at the new specific volume.This approach should work for a reversible process but in this case it seems like the process is irreversible because the spring is providing work. In that case, I'm not sure what the best approach would be.