# why does a hot air balloon float For an ideal gas, the temperature(T), volume(V) and pressure(P) are related by the ideal gas law PV = n*R*T where n is the amount of substance in moles and R is the gas constant. If pressure and amount of substance are constant, the volume is directly proportional to the temperature. As temperature increases so does the volume. A hot air balloon is filled with air at a higher temperature than the surrounding air. The same mass of gas in the balloon occupies a larger volume as compared to the surrounding air. When an object is immersed in a gas, there is a buoyant force exerted on it which is equal to the weight of the gas that it displaces. The weight of the air displaced by a hot air balloon is greater than its own weight. This is the reason why it floats in sky. Though a hot air balloon floats, it does not continue to rise for ever. As it moves up, the pressure of the surrounding air decreases and this decreases the buoyant force on the balloon. It can only rise to a height where the buoyant force is equal to the weight of the balloon.
ItБs one of those basic rules we grow up hearing: hot air rises and cool air sinks, but why is that? If youБve seen our, you know that density is one of the key factors in whether an object sinks or floats in a given substance, but a substanceБs density doesnБt have to remain the same. The secret is in the name itself: air balloon. By altering the temperature of the air inside, we decrease its density, allowing it to float. Since setting off a hot air balloon would be too expensive and a floating lantern is a fire hazard, we showed this same effect by altering the temperature of a helium balloon to prevent it from floating in air. This all ties back to something in physics called the Ideal Gas Law, which can be expressed as PV=nRT; pressure x volume = number of moles of a substance x the gas constant x temperature.

In the case of a hot air balloon and the helium balloon, Бn,Б БR,Б and БPБ are not changing, we can focus on volume and temperature. By decreasing the temperature of the helium balloon, the volume must also decrease. Since density is described as mass divided by volume, as volume decreases, density increases. With enough drop in volume, the helium balloon becomes too dense to float. After being removed from the liquid nitrogen, the balloon slowly heats back up to room temperature.

As it heats up, it returns to its original volume and floats back to the ceiling. The reverse is true in a hot air balloon, with its density starting equal to the air outside it. As the air inside it is heated, its density decreases to the point where it has so much buoyant force lifting up on it that it can lift not only the balloon but the basket and passengers as well. When itБs in the air, the operator has to make sure the air stays at a consistent temperature for them to maintain altitude, with an increase or decrease in temperature will lead to an increase or decrease in altitude respectively.

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