When the air inside a hot air balloon is heated, why does the balloon rise? (Assume the air pressure inside the balloon is equal to the air pressure outside the balloon.)

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When the air inside a hot air balloon is heated, why does the balloon rise? (Assume the air pressure inside the balloon is equal to the air pressure outside the balloon.)
 
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Any object will float or not depends on its density. If the density of object is lower than the density of surrounding medium, the object will float.

 Note that the density of hot air is less than the cold air. Due to this reason, hot air rise above in atmosphere. For example steam.

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