Why do Hot Air Balloons Fly
How the Ideal Gas Law and Archimedes's Principle Apply to Ballooning
Nov 10, 2008
At a hot air balloon festival, hot air balloons slowly fill and then rise majestically in the predawn sky. These hot air balloons fly because of two fundamental principles of physics: the ideal gas law and Archimedes's principle.
Ideal Gas Law
The ideal gas law is a mathematical relationship between the volume pressure and temperature of a gas. For a given quantity of gas, the pressure, P, multiplied by the volume, V, divided by the temperature, T, remains a constant.
If a gas is heated, as in a hot air balloon, then its volume will increase. A heater in the balloon's basket heats the air inside the balloon and blows hot air into the balloon. As the volume of gas increases, it fills the balloon. Soon the balloon is full of hot air. If the air continues to heat up, it expands and flows out of the hole in the bottom of the balloon.
Hence a balloon filled with hot air contains fewer air molecules than the same balloon inflated to the same size with cool air. A hot air balloon will therefore be less dense than a balloon filled with cool air as a consequence of the ideal gas law.
Archimedes's Principle
Archimedes's principle states that when an object is suspended in a fluid, the buoyant force acting on an object is equal to the weight of the fluid displaced. As a consequence of Archimedes's principle, an object will float in a fluid if it is less dense than the fluid.
Ordinarily people think of a fluid as being a liquid, however in science a fluid is defined as either a liquid or a gas. Air is therefore a fluid and Archimedes's principle applies to floating in air as well as floating in a liquid.
Hot Air Balloons
The balloon filled with hot air is less dense than when it is filled with cool air. For the balloon to rise and lift the basket and passengers off the ground, the hot air in the balloon must have a low density. The balloon, basket, and passengers combination must weigh less than the total amount of air displaced by the balloon. Then the upward buoyant force exceeds the downward weight (gravitational force).
Helium filled balloons float by the same principle because helium gas is much less dense than air.
The hot air filling the balloon reduces its density according to the ideal gas law. When its total density is less than the density of air, it floats according to Archimedes's principle.
The density difference is greater when the air temperature is cooler, so hot air balloons are often inflated in the cooler predawn hours.
Enjoy watching hot air balloons soar into the air, or take a balloon flight. Understanding the physics that causes them to silently float upwards increases their beauty. Fundamental physical principles are beautiful to the mind and contribute to visual beauty.
Further Reading
Bloomfield, L.A. How Things Work 3rd ed. Wiley, 2006
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