Question

A closed, rigid, 0.45 m^3 tank is filled with 12 kg of water. The initial pressure is p1 = 20 bar. The water is cooled until the pressure is p2 = 4 bar. Determine the initial quality, x1, and the heat transfer, in kJ.

Answer 1

initial quality = 0.3690

heat transfer = 979.63 kJ/kg

Step-by-step explanation:

Given data:

volume of tank 0.45^3

weight of water 12 kg

Initial pressure 20 bar

final pressure 4 bar

Specific volume
`v = \frac {0.45}{12} = 0.0375 m^3/kg`

At Pressure = 20 bar, from saturated water table

`v_f = 0.01177 m^/kg`

`v_g = 0.099587 m^3/kg`

`x = (v -v_f)/(v_g -v_f) = (0.0375 - 0.001177)/(0.099587 - 0.001177)`

inital quality is x =0.3690

Heat transfer is calculated as

`u_1 = h_f + x(h_g - h_f) = v_f + x( h_(fg))`

from saturated water table, for pressure 20 bar ,

`h_f = 908.79 kJ/kg, h_(fg) = 1890.7 kJ/kg`

=908.79 + 0.0357(1890.7)

= 979.63 kJ/kg