Project ForgeThermodynamics
Entropy & Second Law
GATE 2018
Hard
A tank of volume 0.05 m³ contains a mixture of saturated water and saturated steam at 200°C. The mass of the liquid present is 8 kg. The entropy (in kJ/kg K) of the mixture is __________ (correct to two decimal places). Property data at 200°C: vf=0.001157 m³/kg, vg=0.12736 m³/kg, sfg=4.1014 kJ/kg K, sf=2.3309 kJ/kg K.
2.5 kJ/kg K(± 0.05 accepted)
Explanation
Volume of liquid = 8×0.001157 ≈ 0.009256 m³. Remaining vapour volume = 0.05−0.009256 ≈ 0.040744 m³. Mass of vapour = 0.040744/0.12736 ≈ 0.320 kg. Total mass = 8.32 kg, quality x = 0.320/8.32 ≈ 0.03846. s = sf + x·sfg = 2.3309 + 0.03846×4.1014 ≈ 2.49 kJ/kg K.
Source: GATE ME 2018 Session 1 (Set 1) (2018)
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