Balloon

Narrative
To create a miniature hot air balloon the required materials are: tissue paper, glue sticks, scissors, and a gore template that can be found on the internet. To assemble the balloon the tissue paper must be cut into 8 panels using the gore template. The panels must then be glued onto each other by offsetting one of the panels by 1 centimeter. This step must be repeated until all 8 panels are glued together and form a balloon. The balloon should measure 1.5 meters tall and about ¾ of a meter in diameter along its widest point. Since April, 22nd is Earth day it has been decided to recycle old materials to make our balloon so it will be eco-friendly.

Estimated Volume of the Balloon
Height of Balloon = 1.5 meters
Average Circumference = 238.76 cm
Average Diameter = 76.04 cm = 238.76cm/ πcm
Volume = (4/3)* π * radius³
Volume = (4/3)* π * 38.02³
Volume = 230,210.40 cm³
230,210.40 cm³ * .001 = 230.21 Liters
Volume = 230.21 Liters

Molar Mass of Air
Composition of Air
78.08% Nitrogen = .7808 * 28 = 21.86
20.95% Oxygen = .2095 * 32 = 6.7
.93% Argon = .0093 * 39.9 = .37
.03% Carbon Dioxide = .0003 * 44 = .0132
.002% Neon = .00002 * 20 = .0004
21.86 + 6.7 + .37 + .0132 + .0004 = 28.94grams/Mole of Air

Density of Air
28.94/22.4 = 1.29g/Liter at STP
Formula
Density = [(Molar Mass of Air)*(Pressure)]/[(.08206)*(Temperature)]
Density @ 20ºC = (1*28.94)/ (.08206*293K) = 1.20g/L
Density @ 75ºC = (1*28.94)/ (.08206*348K) = 1.01g/L

Moles of Gas in Balloon @ 75 ºC
Pressure * Volume = moles * .08206 * Temperature
1*230.21 = n(.08206)*348
230.21 = n * 28.56
230.21/ 28.56 = (n * 28.56)/28.56
8.06 moles in the balloon at 75 ºC

Mass of Air in Balloon
(8.06 * 22.4) * 1.01g/L = Mass of Air in Balloon in grams
182.34 grams
Mass of Balloon
34.57 grams
Density of Balloon and Air
182.34g + 34.57g = 216.91g
216.91g/230.21 L = .942g/L

Theory
A hot air balloon rises into the sky because the air inside the balloon is heated up and then the balloon and air inside become less dense than the air around the outside of the balloon. Because the balloon was less dense than the air around it the balloon would float into the sky as long as there were no holes or any other defects in the balloon.

Fun Facts on Hot Air Balloons
Hot Air Balloons were invented in France in the 1700’s
The longest hot air balloon fight ever went from Japan to Canada.
You cannot fly a hot air balloon in the rain because it boils the water and can ruin the balloon’s fabric
People have champagne when they land their hot air balloons because when ballooning began in the late 1700’s they assured the farmers their balloon wasn’t a dragon and to forgive them for landing on their farm land
A sheep, a duck, and a chicken were the first hot air balloon passengers
It was originally thought that smoke, not hot air, was what would lift the balloons into the air. This was concluded by the Montgolfier brothers who put paper in their chimney and saw it float up