Question

A partition divides an insulated tank into two parts. One part of the tank contains 2.5 kg of compressed liquid water at 60°C and 500 kPa while the other part is evacuated. The partition is then removed, and the water expands to fill the entire tank. Determine the final temperature of the water and the volume of the tank for a final pressure of 10 kPa.

Answer 1

`V=0.972m^2`

Step-by-step explanation:

the energy balance is :

`E_(in) -E_(out) =`Δ
`E_(system)`

0=ΔU=
`mm(u_(2) -u_1)`

`u_1=u_2`

the properties of water are from table

`P_1=500 kpa\\T_1=60 degree C\\v_1=v_f_(-->60) =251.6 Kj/Kg`

verified if we get a quantity between 0 and 1

`P_2=10 kpa\\u_2=u_1`

we have,

`v_f=0.001\\v=14.670 m^3/kg\\u_f=191.79\\v_(fg)=2245.4 Kj/Kg\\`

therefore,

`x_2=(u_2-u_f)/(u_(fg) )`

we replace the values in this equation:

`x_2=(251.6-191.79)/(2245.4)\\ x_2=0.026`

so,

`T_2=T_(sat--10kpa) =45.81\\v_2=v_f-x_2v_(fg)`

we replace the values in this equation:

`v_2=0.38886m^3/kg`

we have,

`V=mv_2`

we replace the values in this equation:

`V=0.972m^2`