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## Homework Statement

An amount of water substance having a mass of 1 kg is contained in a vessel at a pressure of 1 MPa. It is heated for some time after which the pressure is 3 MPa. The volume of the vessel is 0.1 m

^{3}. Assuming no work is done by or to the substance, calculate the final temperature of, and the heating done to, the contents of the vessel.

## Homework Equations

I am not sure about them. I believe, they would be:

## m=m_g + m_f ## , ##V=v_f m_f +v_g m_g## and ##PV=nRT## , ##ΔQ+ΔW=ΔU##

*Thermodynamic and transport properties of fluids*.

## The Attempt at a Solution

I have stated that ##m_f+m_g=m=1kg## and ##v_g m_g + v_f m_f = 0.1 m^3##. It is also known that ##P_1=1MPa=10 bar## and ##P_2=30 bar##.

I have attempted to read the value of a temperature from 'Saturated Water and Steam section' for ##P=10bar## which would give me ##179.9°C##. Assuming that volume is constant throughout the whole process as the mixture is in a vessel it gave me ##{\frac{P_2 T_1}{P_1}}=T_2## but it gave me the wrong answer.

I have then tried to obtain the value of ##v_g## for 'Saturated Water and Steam' and it the value would be 0.1944 ##[kg/m^3]##. Solving for ##m_f## and ##m_g## by assuming that since ##m_f+m_g=1kg## and so ##dryness fraction=x=mg/1=mg## did actually either got me nowhere or I just do not know what to do with these values.

I need help to know what kind of assumptions should I use and have I chosen appropriate equations for solving this problem. Thanks