Hot air rises due to the fact that when you warm air (or any type of other gas for that matter), that expands. As soon as the air expands, it becomes less thick than the air about it. The less thick hot air then floats in the an ext dense cold air lot like lumber floats top top water because wood is less dense than water. This floating effect in a less thick medium is called a buoyant pressure or a displacement force.

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We have the right to model what I simply said with a small physics. Consider the air come be suitable gas (this is a good approximation i m sorry neglects the communication of wait molecules through each other).

The pressure P, volume V, lot of gas N, and temperature T can all be related by the best gas equation together P*V=N*R*T where R is the ideal gas constant (8.314 in systems of J/(mol*K)).

Say you begin with an lot of wait N at pressure P, volume V1, and also Temperature T1 and also heat the in a balloon (we will disregard the mass and elastic nature of the balloon for simplicity) come temperature T2.

The right gas equation have the right to be rewritten as P*V1/(N*T1)=R=P*V2/(N*T2) which v a little algebra deserve to be resolved to provide V2=V1*T2/T1.

From this we see that if you warmth a gas such that T2>T1 you get V2>V1 meaning that the gas expands. Now since you have actually the very same amount of gas, the mass walk not change so the density before heating is d1=m/V1 and also the density after heating is d2=m/V2.

Now the pressure of gravity on the warm air (Fg) is offered by the fixed of the hot air time the gravitational consistent g (9.8 m/s2) (Fg=d2*V2*g). Right here the massive of the hot air is offered by the density of the hot air times the volume the the warm air. The buoyant force on the balloon is provided by the fixed of the waiting displaced time the gravitational continuous (Fb=d1*V2*g). Right here the fixed of the wait displace is given by the density of the neighboring cool air time the volume the the balloon (hot air). Currently the buoyant pressure is up and the gravitational pressure is down so the net pressure is offered by F=Fb-Fg=d1*V2*g-d2*V2*g=m*g*(V2/V1-V2/V2) which deserve to be rewritten utilizing the relation from the right gas law (V2=V1*T2/T1) to give: F=m*g*(T2/T1-1).

This equation shows that as you heat the air in the balloon T2>T1 (i.e. T2/T1>1) you obtain a positive pressure (F>0) which method that the pressure is up and also the balloon rises.

In summary, hot air rises because it is less thick than the neighboring air.