Does hot air always rise?

Yes.

The correct answer would be that hot air 'tends' to rise and cold air 'tends' to sink, due to differences in density (cold air is more dense than hot air). But, there are conditions (like a temperature inversion that Gary mentioned) when a layer of cold air on top of a layer of hot air prevents the hot air from rising. Basically, you have the cold air pushing down and the hot air pushing up with the same amount of force. So, it's a stalemate and the hot air can't rise.

Actually, hot air does not rise. Less dense air rises, while more dense air sinks, but in practice, hot air is usually less dense than cold air, so it usually rises. Even this is only true if the hot and cold air are at the same barometric pressure. Temperature, pressure and density are proportional to one another according to the Ideal Gas Law, which shows that warm air is less dense than cold air at the same pressure, and less dense air always rises. If the pressure was different between the two air parcels, however, it would be possible for warm air to be more dense than cold air, and thus the warm air would sink. However, a pressure difference this drastic is extremely rare in nature.

What heats the air is the heating of the earth by the sun, heat mostly passes straight through the atmosphere. Yes, warm air rises, but once it leaves the surface of the earth, and thus the source of the heat it begins to loose energy, and thus loose heat. By the time air gets to the level of a moderate sized mountain, much of the heat in the air is lost, so the air will tend to be cold, since only a little bit of energy from the surface of the mountain is passed into the cold air. Look up the term "adibatic cooling"

All the previous answers are WRONG. It is true that less dense things tend to rise relative to more dense things but hot air does NOT always rise.

There are two factors that have a strong influence on the density of air: temperature and humidity. Yes, gases expand when they are heated but gases also change when the composition of the gases change. You might think that, when an air mass picks up moisture, it is gaining something so it would become more dense but, this is wrong. It makes sense if you think about gases on an atomic/molecular level. Air is a mixture of many gases but is basically 78% N2 + 21% O2 + small amounts of CO2, H2O, He, Ar, SO2, etc. When air picks up humidity, H2O, it becomes less dense because, relatively speaking, an H2O molecule is bigger than N2 or O2 molecules so it takes up more space and it is lighter than N2 or O2 molecules so, increasing humidity means lower density.

This is why we have "temperature inversions" where hot dry air "sinks" or is below (because it is more dense) than cool humid (which rises because it is less dense).

And... When humid air reaches a condition where the humidity changes rapidly (like the water vapor condenses into water droplets), all hell breaks loose. The latent heat of boiling comes out and the density of the air changes (because the humidity changes) and you get updrafts and downdrafts. This is why bright sunny days are high barometric pressure days and why cloudy stormy days are low barometric pressure days.

Yes, hot air is less dense than colder air, thus hot air rises and cold air sinks.

In a 'direct' thermal circulation...'hot' air (positive buoyancy) will rise and cold air (negative buoyancy)will sink; however...there are 'indirect' thermal circulations in the atmosphere brought about by ageostrophic motions where cold air rises and warm air sinks.

Direct: mid-latitude Hadley circulation cell; tropical storms; deep moist convection (thunderstorms); shallow dry convection (fair weather cumulus); entrance region of upper level jet streaks; land / sea breeze;

Indirect: mid-latitude Ferrel circulation cell; exit region of upper level jet streaks

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The 'thumbs down' crowd is apparently confused by even the most basic concepts of dynamic and thermo-dynamic meteorology.

Yes it is(in order to generalize). But in real life its not always the case

Yes, I think so, due to convection current