__Concept:__

The entropy of a mixture:

s = s_{f} + x s_{fg }

where x is the dryness fraction.

\(x = \frac{{{m_s}}}{{{m_f} + {m_s}}}\)

where m_{s} is the mass of the steam and m_{f} is the mass of liquid

V = Vf + Vg

V = mfvf + mgvg

__Calculation:__

Given, mf = 8 kg,

v_{f} = 0.001157 m3/kg, vg = 0.12736 m3/kg

sfg = 4.1014 kJ/kg, K, sf = 2.3309 kJ/kg K

V = V_{f} + V_{g} = 0.05 m^{3}

m_{f}v_{f} + m_{g}v_{g} = 0.05

(8) (0.001157) + m_{g}(0.12736) = 0.05

m_{g} = 0.32 kg

\(x = \frac{{{m_s}}}{{{m_f} + {m_s}}} = \frac{{0.32}}{{8 + 0.32}} = 0.0385\)

s = s_{f} + x s_{fg} = 2.3309 + 0.0385 × 4.1014 = 2.488 kJ/kg