A small research submarine with a volume of 1.2x10 ^5 L has an internal pressure of 1.0 atm and an internal temperature of 150°C. If the submarine descends to a depth where the pressure is 150 atm and the temperature is 30°C, what will the volume of the gas inside be if the hull of the submarine breaks?
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The best way to approach this problem is by using the combined gas law
P
1
V
1
T
1
=
P
2
V
2
T
2
, which relates temperature, pressure, and volume, assuming the number of moles remains constant. Knowing that
P
1
=
1
a
t
m
,
T
1
=
273.15
+
150
=
423.15
K
,
V
1
=
1.2
⋅
10
5
L
,
P
2
=
150
a
t
m
, and
T
2
=
303.15
K
, we get
V
2
=
P
1
P
2
⋅
T
2
T
1
⋅
V
1
=
1
150
⋅
303.15
423.15
⋅
1.2
⋅
10
5
=
573
L
Notice how both a significant increase in pressure and an important drop in temperature contributed to the massive drop in volume the submarine underwent.
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