E234 THERMODYNAMICS
Exam 1 – September 22, 2008
Data:
R = 8.314 J/mol.K
For air R = 0.287 kJ/kg.K
M(air) = 29 kg/kmol
1.
A tank has two rooms at 80.3
o
F separated by a membrane. Room A has 1 kg air and
pressure of 1 bar, room B has 750 L air with a specific volume of 0.83 m
3
/kg. The
membrane is broken and the air comes to a uniform state.
Determine
a.
The total mass of air
b.
The final density of the air
c.
The final pressure in bar and in mmHg
T = 80.3
o
F = 26.83
o
C = 300 K
1 bar
= 10
5
Pa
Initial state:
Tank A: P
A
= 1atm
m
A
= 1kg
T
A
= 300 K
Ideal gas law: V
A
= m
A
R
air
T
A
/P
A
= 0.861 m
3
(watch your units)
Tank B: V
B
= 0.75 m
3
v
B
= 0.83 m
3
/kg
T
B
= 300 K
m = V
B
/v
B
= 0.904 kg
a. m = 0.904 + 1 =1.904 kg
b. density = m/V = 1.904/(0.861 + 0.75) =1.18 kg/m
3
c. Ideal gas law: P = mR
air
T/V = 101.75 kPa
2.
A water heater tank is cylindrical, 1 m tall, and diameter 0.5 m. It is made of a thin
steel sheet covered by a 1.5 cm thick foam insulation with k = 0.025 W/m.K. The
combined convection and radiation effects to the surrounding air are expressed in a
convection coefficient of h = 12 W/m
2
.K. The hot water inside is at 72
o
C and the
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 Spring '09
 GALLOIS
 1 kg, 1 m, 0.5 m

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