Why does a hot air balloon rise up and what would we need to lift 500 kilograms.
When air is heated, it expands and occupies more volume. As the weight of a given volume of cold air is more than the weight of an equal volume of warm air, it leads to a force equal to the difference in their weights, acting upwards. This results in hot air balloons rising up.
If you want to lift 500 kg using a hot air balloon, you would have to heat an amount of air so that the weight of the volume of the heated air in the balloon is less than an equal volume of cold air displaced by the balloon by 500 kg.
Hot air balloon rise in the air due to the property of buoyancy possessed by all liquids and gases including the atmospheric air. The air in the atmosphere tries to push up any object that is present in the atmosphere. This pressure is equal to the weight of volume of air equal to the volume occupied by the object. A hot air balloon has a very large balloon filled with hot air. This hot air lighter than the atmospheric air at normal temperature. As a result the weight of the balloon with the hot air inside it is less than the weight of same volume of atmospheric air. This means that that downward force acting on the balloon due to force of gravity s less than the upward force of buoyancy. This causes the balloon to rise up in the air.
However it is worthwhile noting that as the balloon moves up the atmospheric air around it becomes less dense, causing the net upward force of buoyancy to decrease. When this becomes zero the balloon does not rise up further.
To lift a total load of 500 kilograms in an air balloon it will be necessary to ensure that the volume of air in the balloon and its temperature is such that the weight of hot air in the balloon will be at least 500 kilograms less than equivalent volume of normal atmospheric air.