Why is Hot Air Lighter than Cold Air?

[Skim Halo]

If E=mc^2, why is hot air lighter than cold air? Hot air has more energy and should thus have greater mass and therefore be heavier as weight = mg

 

[.Scott]

At the same pressure, hot air is less dense - there's less of it per volume.
Aside from that, a number of molecules on a hot gas would be heavier than the same number of the same cold gas. But it would be very hard to measure the difference. For E=mc^2, you have an awful lot of E equating to very little m.

 

[Skim Halo]

So it's the fact that the air's volume is not constrained which allows it to expand it's volume and being less dense it rises above the colder denser air.

I would assume then however that if two volumes of air were contact rained in equal sized separate vessels, the hotter air vessel would be infinitesimally heavier?

 

[Drakkith]

I would assume then however that if two volumes of air were contact rained in equal sized separate vessels, the hotter air vessel would be infinitesimally heavier?

Exactly. Given two containers of gas, identical in all respects except for temperature, the hotter one would have a tiny bit more mass than the cooler one.