See the universe through a brand new set of
eyes.
In the first 30 seconds of Mission: Impossible
- Ghost Protocol, a doomed IMF agent is running
across the roof of a tall building.
He's trying to get away from two bad guys
-- a favorite pastime of ALL secret agents.
In his right hand, the agent has a small object
-- an object that is about to get very big,
and very important.
The agent is holding ... Crash Pad in a Can!
Watch what happens...
Crash pad in a can?
Is there any way this could work?
Let's first see if a simple expansion of compressed
gas -- say from a big CO-2 cartridge -- might
do it.
The volume of the object in the agent's hand
-- what I'm calling the "can" or "canister"
-- is no more than 1 liter.
Here's a 1-liter Poke bottle to give you an
idea of how much volume that is.
Oh, I'm sorry.
This isn't a 1-liter bottle of Poke.
This is a 1-liter bottle of Diet Poke.
While 1 liter is a handy unit of volume, it's
not the international standard.
Around the world, in every corner of planet
Earth -- except the corner shaped like THIS
(arg!) -- the official unit of volume is the
cubic meter.
3-dimensional creatures -- and I qualify (barely)
-- SHOULD be familiar with the cubic meter.
It's the volume of space inside a large refrigerator.
So, 1 cubic meter of air would fill an otherwise
empty home refrigerator.
1 cubic meter of water would fill a large
bathtub.
WE need to be familiar with the cubic meter
in order to estimate the volume of the inflated
crash pad.
To the nearest power of ten, the volume of
the crash pad is about 10 cubic meters.
Look at the volume difference between this
1-liter bottle and that 10-cubic-meter crash
pad.
How does THIS become THAT?!
1000 liters fit inside a cubic meter.
1000 of THESE will fit in a big refrigerator
(we'd have to do some cramming, but they'd
go).
1 liter is 1 one-thousandth of a cubic meter.
The 1-liter object in the secret agent's hand
has to increase in volume to 10 cubic meters.
From THIS to 10 refrigerators?!
That's a volume growth factor of 10,000!
Can you imagine what incredible pressure -- of
stuff just itchin' to get out -- there must
be inside such a can?
Well, we can do better than IMAGINE.
We can figure the pressure out!
Let's do something very generous for the makers
of Ghost Protocol: let's assume that the 1-liter
object in the agent's hand contains nothing
but gas that can expand.
Let's ignore the fact that the plastic skin
of the crash pad has to fit in the can, too.
Let's suppose that the crash pad's skin is
so light, so strong, and so VERY thin, that
it takes up NONE of the space in the 1-liter
can.
This is idiotic, I know, but let's be idiots
of generosity when considering what marvelous
high-tech gadgetry the IMF engineers have
invented.
Let's make the situation ideal in another
way, too.
Let's treat the gas that inflates the crash
pad as a so-called "ideal gas."
Then we can turn to the law that describes
the behavior of an ideal gas.
You know what it's called; you learned it
in high school.
It's the ideal gas law: PV = nRT.
But wait, I'm not a chemist, I'm a physics
teacher.
So I'll use the physics teacher version of
the ideal gas law.
That's P = nkT/V.
Why might this be better?
Because now the ideal gas law describes cause
and effect, and you can get a FEEL -- from
the equation ITSELF -- why the law is true.
The effect is gas pressure, P. And there are
three causes of gas pressure: first, the number
of gas atoms, N, flying around; second, the
energy of each atom's flight, kT (k is known
as Boltzmann's constant, and T is the absolute
temperature); and, finally, the volume of
space in which the energetic atoms are confined.
P = NkT/V. Gas pressure is caused by many
atoms, having energy of motion, confined in
a volume.
It makes intuitive sense.
Intuition cannot PROVE a law, but it sure
can help us REMEMBER it: Pressure is caused
by a number of atoms -- each with energy -- confined
to a volume.
P = NkT/V.
Notice that the volume, V, is in the denominator.
This means that the pressure varies INVERSELY
with the volume.
We don't have to worry about N, k, and T in
this equation because they're not changing.
The number of atoms, their temperature, and,
of course, Boltzmann's constant ALL remain
unchanged.
That's because the atoms in the crash pad
all CAME from the can, and both the can and
the crash pad remain more or less at the same
temperature.
So, the ideal gas law is telling us that the
pressure varies inversely with volume.
For example, if the volume doubles, then the
pressure is cut in half.
If the volume triples, then the pressure is
cut by one-third.
And if the volume goes up by a factor of 10,000,
then the pressure goes down by a factor of
one over 10,000.
But the pressure of the gas in the crash pad
is at least 1 atmosphere.
How can THAT be 10,000 times LESS than the
gas pressure in the 1-liter can?
The pressure in the can must be 10,000 atmospheres
-- 10,000 times ordinary atmospheric pressure!
A can made of STEEL will explode at about
100 atmospheres.
But this Mission Impossible canister mustn't
just withstand twice as much pressure; not
just ten times as much pressure, but rather
100 times as much pressure!
But wait: What if the gas that inflates the
crash pad is not simply expanding?
What if the gas is -- in a sense -- CREATED
... by a chemical reaction in the canister.
Professor Zare tells us that this is how some
car airbags and airplane escape chutes work.
They inflate under the pressure of nitrogen
gas generated by the decomposition of solid
sodium azide.
But again, says the good professor, there's
not enough room in the 1-liter canister for
the atoms that must turn into 10 CUBIC METERS
of gas at normal temperature and pressure.
No mater how special our chemical reaction
is, THAT much change in volume is impossible.
*** When ANY solid or liquid becomes ANY gas
at room temperature and pressure, a volume
increase of about 1,000 is the most we can
possibly expect.
Or, looking at it in reverse, there's no way
to stuff 10 cubic meters of gas atoms into
a 1-liter canister without crowding the atoms
together in a way that violates the laws of
chemistry and of quantum physics.
Ah, but wait, is there yet another possibility?
Not the simple expansion of compressed gas.
Not a fancy chemical reaction that produces
gas from a solid or liquid.
But how about a PHYSICAL EFFECT that draws
SURROUNDING air into the crash pad?
Perhaps something called the Venturi effect
-- an aspect of Bernoulli's Principle -- is
involved.
Look at this...
The rapid expansion of an airplane emergency
slide is STARTED by the expansion of simple
compressed gas.
But the high speed flow of THIS gas draws-in
SURROUNDING air to join it.
We examine Bernoulli's Principle (and its
so-called Venturi effect) in another video.
So, the emergency slide fills with compressed
gas but, even more so -- MUCH more so -- with
local ambient air.
According to Wikipedia, 2000 times more air
(by volume) can be drawn into the slide than
existed in the original compressed-gas canister.
That's good.
That's even amazing.
But it's still not enough.
We need the growth factor to be at least 10,000,
not 2,000.
Close but no cigar.
And when we consider the obvious need to get
the crash pad cover -- the plastic skin -- into
the 1-liter canister, we know it's crazy.
The IMF engineers are good, but they're not
THAT good.
Mission Impossible?
Well, crash pad in a can may not be impossible.
But THAT big a crash pad in THAT small a can
sure seems to be.
