Intro thermodynamics question (simple piston cylinder)

[slashrulez]

Homework Statement

A mass of 5 kg of saturated liquid -vapour mixture is contained in a piston-cylinder
device at 100 kPa (see Figure 1). Initially 2 kg of water is in the liquid phase and the
rest is in the vapour phase (State 1). Heat is transferred to the water and the piston,
which is resting on a set of stops, starts moving when the pressure inside reaches 200
kPa (State 2). Heat transfer continues until the total volume is increased by 25% (State
3).

(2) (a) Find the temperature in State 1.
(4) (b) Determine the volume in State 1.
(4) (c) What is the temperature in State 3?
(3) (d) Is State 2 in the 2-phase region or in the superheated vapour region?
(4) (e) Show the process on a P-v diagram with respect to the saturation lines; points
1-3 must be labeled and the direction of the process indicated.
(3) (f) What is the work done during this process?
(5) (g) Calculate the total heat transferred to the system.

No need to include the figure, it's pretty much a piston sitting on some stops.

Homework Equations

Errmm...none I think

The Attempt at a Solution

My question is in regards to part c, and then part e. I know that in state 2 it's a superheated vapour because I know the pressure, so I can compare specific volumes and whatnot. My problem is that I don't really know how to find anything about state 3 with the info given. All I know is that the volume goes up, so I can find the new specific volume, but past that I don't know. I don't have any info about the pressure, and all I know is that the temperature is probably more than it is in state 2. I want to assume the pressure stays constant between 2 and 3, since I could work with the specific volume and pressure to figure out the temperature pretty easily, but I don't know if I can assume that without the question stating it. As for part e, I can't really calculate boundary work without knowing the pressure, so figuring out c will probably make it straightforward.

So pretty much I'm thinking that I can assume the pressure stays constant during the expansion. Other than that, I have no idea

 

[slashrulez]

Going to add another question that's been giving me some difficulty.

4. Ethylene, C2H4, enters an adiabatic turbine at 10.24 MPa and 339 K (State 1). The
ethylene exits the turbine at 228 K with a quality of 95% (State 2a).
Data for ethylene:
Tc = 282.4 K
Pc = 5.12 MPa
R = 0.2964 kJ/(kg.K)
Cp0 = 1.5482 kJ/(kg.K)
Use the generalized charts to calculate the following:
(5) (a) The specific volume of the ethylene at the inlet of the turbine, in m3/kg.
(10) (b) The work output of the turbine, in kJ/kg.
(10) (c) The quality at the exit of an isentropic turbine operating between the same
inlet conditions and the same exit pressure as the turbine above (State 2s).

(a) I think I know how to do this. I just set up Pv = ZRT and figured out Z from the lee-kesler diagram, then solved for v

(b) I'm not sure on this. I mean, I assume I should start with Q - W = del U, and since it's adiabatic I just need to find the change in internal energy. At first I thought I would need to use the charts to do some type of enthalpy/entropy departure calculation, but none of that relates to internal energy. My only other guess is to say R = Cp - Cv and solve for Cv, and then say del U = Cv(T2 - T1). That seems way too easy to me, plus I'm guessing the first relation only works for ideal gases, but I think the second relation would hold since I don't think my volume is changing. Another thing that worries me is that I never used the quality given in the question, so unless they put it in there to trick me I might be missing something.

(c) This part really has me confused, although I haven't really put much work into it. If the turbine is already adiabatic, would it being reversible change anything? And if so, I really have no idea how to go about solving this. I'm guessing I would need to use the entropy departure chart thing, but I really don't know beyond that. I was also thinking of using the relationships T2/T1 = (P2/P1)^[(k-1)/k] and T2/T1 = (v1/v2)^(k-1) where k = Cp / Cv, but again that's based on me deriving Cv, and I'm not even sure if that would get me anywhere. I was just thinking that if I knew the specific volume, temperature and pressure, quality wouldn't be too hard to get. Not sure how to do it with a non-ideal gas though