Concept:
The entropy of a mixture:
s = sf + x sfg
where x is the dryness fraction.
\(x = \frac{{{m_s}}}{{{m_f} + {m_s}}}\)
where ms is the mass of the steam and mf is the mass of liquid
V = Vf + Vg
V = mfvf + mgvg
Calculation:
Given, mf = 8 kg,
vf = 0.001157 m3/kg, vg = 0.12736 m3/kg
sfg = 4.1014 kJ/kg, K, sf = 2.3309 kJ/kg K
V = Vf + Vg = 0.05 m3
mfvf + mgvg = 0.05
(8) (0.001157) + mg(0.12736) = 0.05
mg = 0.32 kg
\(x = \frac{{{m_s}}}{{{m_f} + {m_s}}} = \frac{{0.32}}{{8 + 0.32}} = 0.0385\)
s = sf + x sfg = 2.3309 + 0.0385 × 4.1014 = 2.488 kJ/kg