Respuesta :
Answer:
The pressure and volume of the tank are 246.878 Kpa and 9.449 m³ respectively.
Explanation:
Volume is constant as the tank is rigid. Take the saturation condition of water from the steam table for pressure at 127°C.
Given:
Total mass of water is 22 kg.
Mass of liquid water is 9 kg.
Temperature of water is 127°C.
From steam table at 127°C:
The pressure in the tank is 246.878 Kpa.
Specific volume of saturated water is 0.00106683 m³/kg.
Specific volume of saturated steam is 0.72721 m³/kg.
Calculation:
Step1
From steam table at 127°C:
The pressure in the tank is 246.878 Kpa.
Step2
Dryness fraction is calculated as follows:
[tex]x=\frac{m_{v}}{m_{t}}[/tex]
Here, dyness fraction is x, mass of vapor is [tex]m_{v}[/tex]and total mass is [tex]m_{t}[/tex].
Substitute the values in the above equation as follows:
[tex]x=\frac{m_{v}}{m_{t}}[/tex]
[tex]x=\frac{22-9}{22}[/tex]
x = 0.59
Step3
Specific volume of tank is calculated as follows:
[tex]v=v_{f}+x(v_{g}-v_{f})[/tex]
[tex]v=0.00106683+0.59(0.72721-0.00106683)[/tex]
[tex]v=0.00106683+0.42842447[/tex]
v=0.4295 m³/kg.
Step4
Volume is calculated as follows:
[tex]V=v\times m_{t}[/tex]
[tex]V=0.4295 \times22[/tex]
V=9.449 m³.
Thus, the pressure and volume of the tank are 246.878 Kpa and 9.449 m³ respectively.
