1
Chemical Engineering 140 October 1, 2010
Midterm #1 Solutions
1 a. As liquid drains, air expands, and the pressure in the tank declines. One of two cases
arises. Eventually, the liquid may completely drain, and the air pressure in the tank
matches atmospheric. However, it is also possible for the gas to expand to atmospheric
pressure while some liquid remains in the tank. For large initial gas volume (large α) and
for large initial pressure (large β) we expect complete drainage. For small α and small β,
air remains in the tank.
b. The final pressure is atmospheric, Pa
c. Let n represent the moles of gas. Mass balance reads
dn/ dt 0 so n(t) =n(0)= constant
(1)
d. Since the initial pressure and gas volume are known and since the gas is ideal and
isothermal, we can re-express Eqn. 1 as
Ga
PV P V
(2)
where VG is the gas volume. Since the final pressure is atmospheric, the final gas volume
is
G
V ( ) V
(3)
Clearly, the maximum gas volume is when the tank is completely empty of liquid.
Thus, if
1
, gas remains in the tank. If
1
, liquid completely drains
e. Let VL represent the volume of liquid in the tank. Since liquid is incompressible, mass
balance reads
La
dV / dt k( P P )
(4)
f. We must re-express Eqn. 4 in terms of pressure. Since
GL
V V V
, Eqn. 4 is
combined with Eqn 2 to read
Gaa
2
dV 1
PV dP / dt k( P P )
dt P
(5)
or
