TITLE.PM5

PROPERTIES OF PURE SUBSTANCES 81

Dharm
\M-therm/th3-1.p65

Solution. Capacity of the spherical vessel, V = 0.9 m^3

Pressure of the steam, p 1 = 8 bar

Dryness fraction of steam, x 1 = 0.9

Pressure of steam after blow off, p 2 = 4 bar

Final pressure of steam, p 3 = 3 bar.

(i)The mass of steam blown off :

The mass of steam in the vessel

m 1 =xvV

1 g 1

09

=09 024×

.

.. = 4.167 kg ( At 8 bar : 0.24 m / kg)

Q vg=^3

0.9 m

Capacity

3

Spherical

vessel

Valve

Fig. 3.12

The enthalpy of steam before blowing off (per kg)

= hf 1 + xh 1 fg 1 = 720.9 + 0.9 × 2046.5 ...... at pressure 8 bar

= 2562.75 kJ/kg

Enthalpy before blowing off = Enthalpy after blowing off

∴ 2562.75 = ()hxhf 22 + 2 fg at pressure 4 bar

= 604.7 + x 2 × 2133 ...... at pressure 4 bar

∴ x 2 =2562.75 604.7−

2133

= 0.918

Now the mass of steam in the vessel after blowing off,

m 2 =0 918 0 462..^09 ×. = 2.122 kg [vg 2 =0.462 m / kg.......at 4 bar]^3

Mass of steam blown off, m = m 1 – m 2 = 4.167 – 2.122

= 2.045 kg. (Ans.)

(ii)Dryness fraction of steam in the vessel after cooling, x 3 :

As it is constant volume cooling

∴ xv 2 g 2 (at 4 bar) = xv 3 g 3 (at 3 bar)