Answer:
Part a: The volume of vessel is 4.7680
and total internal energy is 3680 kJ.
Part b: The quality of the mixture is 90.3% or 0.903, temperature is 120 °C and total internal energy is 4660 kJ.
Explanation:
Part a:
As per given data
m=2 kg
T=80 °C =80+273=353 K
Dryness=70% vapour =0.7
<em>From the steam tables at 80 °C</em>
Specific volume of saturated vapours=v_g=3.40527 ![m^3/kg](https://tex.z-dn.net/?f=m%5E3%2Fkg)
Specific volume of saturated liquid=v_f=0.00102 ![m^3/kg](https://tex.z-dn.net/?f=m%5E3%2Fkg)
Now the relation of total specific volume for a specific dryness value is given as
![v=v_f+x(v_g-v_f)](https://tex.z-dn.net/?f=v%3Dv_f%2Bx%28v_g-v_f%29)
Substituting the values give
![v=v_f+x(v_g-v_f)\\v=0.00102+0.7(3.40527-0.00102)\\v_f=2.38399 m^3/kg](https://tex.z-dn.net/?f=v%3Dv_f%2Bx%28v_g-v_f%29%5C%5Cv%3D0.00102%2B0.7%283.40527-0.00102%29%5C%5Cv_f%3D2.38399%20m%5E3%2Fkg)
Now the volume of vessel is given as
![v=\frac{V}{m}\\V=v \times m\\V=2.38399 \times 2\\V=4.7680 m^3](https://tex.z-dn.net/?f=v%3D%5Cfrac%7BV%7D%7Bm%7D%5C%5CV%3Dv%20%5Ctimes%20m%5C%5CV%3D2.38399%20%5Ctimes%202%5C%5CV%3D4.7680%20m%5E3)
So the volume of vessel is 4.7680
.
Similarly for T=80 and dryness ratio of 0.7 from the table of steam
Pressure=P=47.4 kPa
Specific internal energy is given as u=1840 kJ/kg
So the total internal energy is given as
![u=\frac{U}{m}\\U=u \times m\\U=1840 \times 2\\U=3680 kJ](https://tex.z-dn.net/?f=u%3D%5Cfrac%7BU%7D%7Bm%7D%5C%5CU%3Du%20%5Ctimes%20m%5C%5CU%3D1840%20%5Ctimes%202%5C%5CU%3D3680%20kJ)
The total internal energy is 3680 kJ.
So the volume of vessel is 4.7680
and total internal energy is 3680 kJ.
Part b
Volume of vessel is given as 1.6
mass is given as 2 kg
Pressure is given as 0.2 MPa or 200 kPa
Now the specific volume is given as
![v=\frac{V}{m}\\v=\frac{1.6}{2}\\v=0.8 m^3/kg](https://tex.z-dn.net/?f=v%3D%5Cfrac%7BV%7D%7Bm%7D%5C%5Cv%3D%5Cfrac%7B1.6%7D%7B2%7D%5C%5Cv%3D0.8%20m%5E3%2Fkg)
So from steam tables for Pressure=200 kPa and specific volume as 0.8 gives
Temperature=T=120 °C
Quality=x=0.903 ≈ 90.3%
Specific internal energy =u=2330 kJ/kg
The total internal energy is given as
![u=\frac{U}{m}\\U=u \times m\\U=2330 \times 2\\U=4660 kJ](https://tex.z-dn.net/?f=u%3D%5Cfrac%7BU%7D%7Bm%7D%5C%5CU%3Du%20%5Ctimes%20m%5C%5CU%3D2330%20%5Ctimes%202%5C%5CU%3D4660%20kJ)
So the quality of the mixture is 90.3% or 0.903, temperature is 120 °C and total internal energy is 4660 kJ.