# Charles Law - Hot Air Balloons

Concepts to Investigate: Charles's Law, hot air balloons, buoyancy, density, temperature-volume relationships in gases, Archimedes' Principle.

Materials: Tissue paper, scissors, glue, construction paper or other heavy paper, hair dryer.

Principles and Procedures: Frenchmen Joseph and Étienne Montgolfier are credited with the development of the first practical hot air balloon. In September of 1783 they sent a sheep, rooster and duck aloft over Versailles, and two months later sent three men (Jean-François Pilâtre de Rozier, François Laurent, and Marquis d'Arlandes) on a 5.5 mile (approximately 9 km) flight over Paris! Later, hot air balloons were used in the Napoleanic and American Civil Wars to perform reconnaissance of enemy positions and movements. Ballooning is a popular sport today, although propane has replaced hay as a heating fuel, and lightweight nylon and other synthetics have replaced silk, cotton and wool as balloon fabric. In this activity you will employ the principles used by the Montgolfier brothers and modern ballooning enthusiasts in the construction and flight of your own hot air balloon.

Four years after the success of the Mongolfier brothers, fellow countryman Jacques Charles formalized the principle

responsible for balloon flight. Charles's Law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to the absolute temperature (V=kT). For example, if the absolute temperature of a fixed mass of gas (at constant pressure) is doubled, the volume doubles and the density is cut in half (density = mass/volume). If the temperature is raised from room temperature (20˚C, 68˚C, 293 K) to 50˚C (122˚F, 323 K), the volume of the heated air increases 10% (323K/293K= 1.10). Since a hot-air balloon is an open system at constant pressure, this can be accomplished only if air leaves the balloon. Thus, the mass of air remaining in the balloon decreases, leading to a decrease in the composite density of the balloon (balloon and the air it contains). The balloon rises because it now has a lower density than the air surrounding it.

Figures Q-U shows the plans for a pentadecahedronal (15-sided) balloon. Cut five 50 x 130 cm panels of tissue paper and fold each in the middle lengthwise as shown (Figures Q-S). Cut the shaded portions out and place one panel on a large flat surface. Place a second panel over it so all but 3 cm of tissue paper along one border are overlapping (Figure T). Smear white glue down the margin of the top panel and then fold the border of the bottom panel onto the glue to seal the seam. Repeat this process with all five panels until the pentadecahedron is complete (Figure U). Glue a strip of construction paper or other heavy paper around the base of the balloon. Punch three holes in this paper and suspend a small paper clip by threads as shown (Figure U). One student should steady the balloon while the other heats the air inside with a hair dryer (Figure V). You may release the balloon when the top gets quite warm. Compete with other students to see whose balloon goes the highest and stays aloft the longest.

Questions:

(1) How high did your balloon travel? How long did it stay aloft?

(2) Will your balloon rise faster on a cool day or a warm day? Explain.

(3) Why does the hot air balloon eventually fall back to earth?

(4) Why does the density of the air in the balloon decrease as it is heated?