5-32
5-42 Two tanks initially separated by a partition contain steam at different states. Now the partition is
removed and they are allowed to mix until equilibrium is established. The temperature and quality of the
steam at the final state and the amount of heat lost from the tanks are to be determined.
Assumptions 1 The tank is stationary and thus the kinetic and
potential energy changes are zero. 2 There are no work
interactions.
Analysis (a) We take the contents of both tanks as the system.
This is a closed system since no mass enters or leaves. Noting
that the volume of the system is constant and thus there is no
boundary work, the energy balance for this stationary closed
system can be expressed as
E E
in
out
Net energy transfer
by heat, work, and mass
Qout
TANK B
3 kg
150qC
x=0.5
TANK A
2 kg
1 MPa
300qC
'Esystem
Q
Change in internal, kinetic,
potential, etc. energies
>m(u 2 u1 )@A >m(u 2 u1 )@B
'U A 'U B
(since W
KE = PE = 0)
The properties of steam in both tanks at the initial state are (Tables A-4 through A-6)
P1, A
1000 kPa ½°v 1, A
¾
300qC °¿u1, A
T1, A
0.25799 m 3 /kg
2793.7 kJ/kg
150qC ½ v f 0.001091, v g 0.39248 m 3 /kg
¾
u fg 1927.4 kJ/kg
0.50
¿ u f 631.66,
T1, B
x1
v 1, B
v f x1v fg
u1, B
u f x1u fg
0.001091 >0.50 u 0.39248 0.001091@ 0.19679 m 3 /kg
631.66 0.50 u 1927.4 1595.4 kJ/kg
The total volume and total mass of the system are
V
V A V B
m
m A mB
m Av 1, A m Bv 1, B
3 2
(2 kg)(0.25799 m 3 /kg) (3 kg)(0.19679 m 3 /kg) 1.106 m 3
5 kg
Now, the specific volume at the final state may be determined
v2
V
m
1.106 m 3
5 kg
0.22127 m 3 /kg
which fixes the final state and we can determine other properties
P2
v2
T2
½°
¾ x2
0.22127 m3/kg °¿
u2
300 kPa
Tsat @ 300 kPa 133.5 qC
v2 v f
0.22127 0.001073
vg v f
u f x2u fg
0.3641
0.60582 0.001073
561.11 0.3641 u 1982.1 1282.8 kJ/kg
(b) Substituting,
Qout
'U A 'U B
>m(u 2 u1 )@A >m(u 2 u1 )@B
(2 kg)(1282.8 2793.7)kJ/kg (3 kg)(1282.8 1595.4)kJ/kg
or
Qout
3959 kJ
3959 kJ
PROPRIETARY MATERIAL. © 2008 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
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