# Air vs. Helium Balloon

```Nuclear Weapons (and Energy)
the how, the what … and why?
Phys 1020, Day 25:
Questions?
Finish buoyancy
Nuclear Weapons Blmfld 16.1
Reminders:
work on projects
1
Air vs. Helium Balloon
SAME
VOLUMES
AIR
HELIUM
Fbuoyancy
Weight =
mg
Same volume so same Fbuoyancy = upwards net force from pressure of air surrounding
balloon.
How does the pressure inside each balloon compare?
a. Pressure in Air &gt; Pressure in He
b. b. Pressure in Air &lt; Pressure in He
c. Pressure in Air = Pressure in Helium
c. Pressure in Air = Pressure in Helium….
Both are equal to air pressure in the room! Pressure pushing in = pressure
pushing out or else bag will collapse.
How do the number of He atoms compare to number of Air molecules in each
balloon?
a. # Air Molecules &gt; # He atoms
b. # Air Molecules &lt; # He atoms
2
c. # Air Molecules = # He atoms
Review: Air vs. Helium Balloon
AIR
HELIUM
How do the number of He atoms compare to number of Air molecules in each
balloon?
P = k * (# molecules) * Temperature
c. # Air Molecules = # He atoms….
Volume
Ideal Gas Law:
Balloons have same volumes … same pressure … same temperature of gas …
so have same # of gas particles.
See simulation for diff molecules at same temperature
Air molecules heavier, but slower
He atoms lighter, but faster
3
Another useful sim
4
So we could use He Balloon to lift stuff! (Pressures balance)
fat air atoms,
N- 14 neutrons &amp; protons
O- 16 neutrons and protons
little helium atoms, only
2 protons and
two neutrons each.
Much less mass.
Same number of gas particles in each balloon.
But weight of each He particle is less…
5
As the Helium balloon rises…
a.
b.
c.
d.
e.
the volume of the balloon increases
the Fbuoyancy increases
the pressure inside the balloon increases
a and b
a, b, and c
6
BALLOON AT 42 KM ALTITUDE!
a. The volume of the balloon increases!!!
Pressure of surrounding air decreases
Balloon expands until
pressure inside = pressure outside
P = k * (# molecules) * Temperature
Volume
Same # He molecules inside,
to decrease P, volume increases!
Fbuoyancy does not increase.
Volume is much bigger, but density of surrounding air is less
Fbuoyancy is weight of displaced air:
= Volume of balloon x density of air displaced by balloon x g
Volume increases but air density decreases!
7
Summary thoughts
1. Displaced stuff determines Fbouyancy
F buoyancy
1
?
2. Inside stuff determines weight
2
Weight of gas
Fgrav = W = mg
3. Fnet = Fbouyancy - Fgrav
3
Pocket of gas
4. Difference in Pressure =k (N/V) T inside
/ outside --&gt; force on walls
4
8
A look at hot air
What will happen if we heat a beaker of air, and then remove
the stopper?
a. nothing, the air will just stay
there but get hotter
b. there will be fewer molecules
inside because some will be
pushed out into the room
c. the molecules inside will
become lighter because they are
hotter
d. there will be fewer molecules
inside because heating destroys
some of them.
9
Lower T, lower P outside
Higher T, higher P inside
Answer is b. Atoms push out into room until
pressure inside and out is the same
P= k (# molecules/Volume) T
lower
higher
Hot air has fewer atoms in same volume, but same pressure.
10
293 K
1.25 kg/m3
293 K
1.25 kg/m3
Air at 20 Celcius
Air at 70 Celcius
If air inside balloon is heated so that it is 50 C hotter than before, how
does the number of air molecules inside balloon change? What is
ratio of number of air molecules of hotter balloon to number of air
molecules of colder balloon?
P = k * (# molecules) * Temperature
a.
b.
c.
d.
e.
# air hot / # air cold = 70 C / 20 C
Volume
# air hot / # air cold = 20 C / 70 C
# air hot / # air cold = 293 K / 343 K
# air hot / # air cold = 343 K / 293 K
I do not really understand how to reason through this.
11
293 K
1.25 kg/m3
293 K
1.25 kg/m3
Air at 70 Celcius
Air at 20 Celcius
Answer is c: # air hot / # air cold = 293 K / 343 K
P = k * (# molecules) * Temperature
Volume
When heating:
NOT CHANGING:
volume, pressure
CHANGING:
temperature, # of molecules
all constant during heating
P * V = (# molecules) * T
k
At 293 K:
At 343 K:
(# cold) * Tcold = (# hot) * Thot
(# hot)/(#cold) = Tcold/Thot
12
293 K
1.25 kg/m3
Fbuoy
So how do the numbers work out for making a real hot air balloon
(at + 50 degrees)?
Net force upwards = Fbuoy – Weight of air inside (neglect material)
Fbuoyancy= (density of air) (volume) (g)
= (1.25 kg/m3) * (5 m3 ) (9.8 m/s2 ) = 61.25N
weight = mg
Density of hot air:
# hot air molecules = # air molecules cold x (293K /343 K)
Volume
Volume
Weight of air inside = density of hot air x volume x g
= (1.25 kg/m3 * 293 K/343K) * 5 m3 * 9.8 m/s2
= 52.3 N
Lift = Fbouy- W = 61.25N - 52.3N = 8.95N
13
So to lift LESS than 1 kg would need a volume of 5 m3!
If I stick a balloon full of air into liquid nitrogen and wait for some
time, then …. (Liquid Nitrogen temp = 77 K)
a.
b.
c.
d.
e.
number of molecules inside balloon will be less
pressure inside the balloon will be lower
volume will decrease
b and c
a and b
14
Fbuoy
Weight
P= k gas T
T down, P down initially so gets squished in by air around it
until (# air molecules / Volume) or density of particles (gas)
so big that P inside balloon = P in room.
With particle (number density) is so large,
mass density is large also:
Mass = 1.25 kg/m3 * (293 K / 77 K) ~ 3 times higher than air in room
Fbuoy &lt; &lt; weight, drops like rock!
15
Bottle filled with hot liquid, sealed
and then allowed to cool
Bottle filled with hot liquid, sealed
and then allowed to cool
Why does this happen as it cools?
a. Walls of bottle collapsed due to heat
b. Pressure of the air outside is higher
than pressure of air inside
c. Liquid and air inside is pulling sides in
from the inside
b. Air inside cools.. Lowers pressure inside, so
force of air pressure pushing out less than
force of air pressure pushing in.
Walls cannot sustain pressure difference,
Volume decreases until pressure inside
pushing out equals pressure outside, or until
walls can sustain pressure difference.
16
Suction Cup Strength?
A
B
The diameter of Suction Cup B is twice as big as the diameter of Suction Cup A. How
much weight can each suction cup hold?
a. A and B can support the same amount of weight
b. A can support about 2 x more weight than B
c. A can support about 4 x more weight than B
d. B can support about 2 x more weight than A
e. B can support about 4 x more weight than A
17
Suction Cup Strength?
A
B
Pushed many
air molecules
out of here
Force up =
Air pressure X Area
Force down =
Mass of weight
x gravity
The diameter of Suction Cup B is twice as big as the
diameter of Suction Cup A. How much weight can each suction cup hold?
b. B can support about 4 x more weight than A
Area of suction cup = pi * r2
Area of B is 4 times Area of A
Force upwards from air molecules colliding with suction cup = Pressure * Area
18
1. What keeps a suction cup against the wall?
a. sticky rubber, b. electrical attraction between oppositely charged particles,
c. the force of air pressure, d. the buoyancy force, e. magic
2. You remove a partially filled sealed container of food from the refrigerator
and let it warm up. You notice that the lid bows out as it warms up. This is
because:
a. as the food warms it produces gases that increase the pressure inside.
b. the pressure on the outside of the container decreases as the container
warms
c. the air pressure in the room is higher than in the cold refrigerator
d. as the gas inside the container warms up it increases the pressure.
3. A hot air balloon can lift more on
a. a hot day, b. a cold day, c. there is no difference
ans. 1 c, 2. d, 3. b.
19
Group Buoyancy Question – related to lab
Ship loaded with gold in canal lock (water can’t move in or out),
there’s a mutiny and the gold is thrown overboard. What
happens to the water level in the lock? (Assume no water
splashes out)
a. Goes up
b. Goes down
c. Stays the same
Nuclear Weapons*
release of ENORMOUS amounts of energy stored
in the nuclei at center of atoms.
http://kuroiso.org/a005.html
I. “Atomic” bomb (actually “fission” bomb) today
a. how nuclei are held together, why so much energy involved.
b. how they come apart and release LOTS of energy.
alpha decay, neutron-induced fission
c. how to make a whole bunch of them do it at once
= LOTS x whole bunch= bomb
half-life
III. Fusion bomb (little nuclei stick together).
* don’t try this at home
21
Recipe- how to make an atom:
Ingredients: 1 pinch of protons
1 pinch ofneutrons
1 cup of electrons
Proton (positive charge)
Neutron (no charge)
Electron
(negative charge)
1.
2.
Mix protons and neutrons thoroughly.
Bake at 100 million degrees until sticks together
to form solid dense nucleus (about .0000001 s).
3. Frost with lightly with
fluffy layer of negative electrons.
4. Chill before serving!
atom size:
10,000 times smaller
than nucleus-electron
distance
22
Each element has different number of protons.
Atom ingredients:
Proton (positive charge) – charge = 1.6 x 10-19 Coulombs
mass = 1.66 x 10-27 kg.
Neutron (no charge) – no charge
mass = 1.66 x 10-27 kg.
Electron (negative charge) – charge = -1.6 x 10-19 Coulombs
mass = 9.10 x 10-31 kg.
hydrogen
1p
deuterium
1 p, 1n
helium
2 p, 2 n
Uranium 238
92 p, 146 n
23
```