Thermo: Give complete written solution and picture (4) Thermo: Give complete wri
ID: 2997260 • Letter: T
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Thermo: Give complete written solution and picture (4)
Thermo: Give complete written solution and picture (4) Problem 4 Consider the 100 L Dewar (a rigid double-walled vessel for storing cryogenic liquids) shown in the figure. The Dewar contains nitrogen at 1 atm, 90% liquid and 10% vapor by volume. The insulation holds heat transfer into the Dewar from the ambient to a very low rate of 5 J/s. The vent valve is accidentally closed, so that the pressure inside slowly rises due to the heat transferred from the surroundings. It is estimated that the Dewar will rupture when the internal pressure reaches 500 kPa. How long will it take to reach this pressure?Explanation / Answer
State 1: T1 = 77.3 K, Vliq1 = 0.9 V, Vvap1 = 0.1 V
From Table v1f = 0.00124 m3/kg, v1g = 0.21639 m3/kg,
Therefore State 1: T1 = 77.3 K, Vliq1 = 0.9 V, Vvap1 = 0.1 V
mtot = mliq1 + mvap1 = 72.6268 kg;
x1 = 0.0462 / 72.6268 = 0.000636
u1 = -122.27 + 0.000636x177.04 = -122.16 kJ/kg
v1 = 0.1/ 72.6268 = 0.001377 m3/kg
Process: v2 = v1 @ vf at T @ 93.4 K,
from Table , Pg = 483 kPa
State 2: P2 = 500 kPa, Compressed liquid at 93.4 K (use sat. liq.).
Once in the
liquid region then v is not strong function of P.
u2 = -88.108 - 500 x 0.001377 = -88.797
Q2 = 72.6268 x(-88.797 - 122.16) = 2423 kJ
Finally ,time required will be t = Q2/Q
= 2423/(0.005 x 3600) = 134.6 h
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