Thermofluids question, saturated water, piston-cylinder.

[CeilingFan]

Homework Statement

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Hi, not sure if I posted this in the correct section... I have a solution, but am unsure if I am correct in going about it. The answer is not given, so I am having trouble figuring if I'm right or not.

Anyway, the question goes like this.

Saturated water mixture initially in a piston-cylinder device with a stopper.

Initial state: Volume, V₁ = 0.00078539 m^3
Quality, x = 0.85
Pressure, P₁ = 125 kPa

Heat is then introduced, after which the piston hits the stopper. The heating is continued until the pressure reaches 200 kPa.

Final state: Volume, V₂ = 2V_i = 0.00157079
Pressure, P₂ = 200 kPa

a) Find the initial temperature and mass of the liquid.

b) How is the final state, and what is its temperature?

The Attempt at a Solution

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a) I used the provided saturated water table, to find T_sat for P = 125 kPa, and got 105.97C.

For the mass of the liquid, I used x = (v₁ - v_f) / (v_g - v_f), where required values are retrieved from the table.

which gave v₁ = 1.1689 m^3/kg

Mass of entire mixture, m_t = V₁/v₁ = 0.00067191 kg

x = (m_t - m_L) / m_t

m_L = 0.00010078 kg

b) For the final state, I checked the saturated table for P = 200 kPa and found that the specific volume of the substance in question is more than that of saturated vapor at 200 kPa, so using that logic I deduced the final state to be superheated vapor.

v₂ = V₂ / m_t

The temperature is then interpolated from the superheated vapor table at 200 kPa using the specific volume.

It was about 740 degrees celcius.

** Additional thought

Also, if the question required me to think about the state just as the piston hits the stopper, do I use P = 125 kPa, to find the specific volume and compare it with that in the saturated water table? So if v > v of gas --> superheated vapor?

 

[Chestermiller]

I checked your solution, and it is correct. As far as your additional thought is concerned, you don't have enough information. You do know the average specific volume when it hits the stopper, but you don't know what the temperature or the pressure is.

Chet