Why does hot air rise?

We all know that hot air rises and cold air sinks. We also know that hot air rises because it is lighter than cold air, but why is it lighter than cold air? The answer is fairly trivial. To aid thinking it is useful to ask why water sinks and oil rises. It is immediately clear that the density of oil is more than water. The rest, however important, is ironing out the details. So, here’s an overview: if you fill a balloon with hot air, it would expand. But why does hot air rise?

Ooh, look at that Jack Daniels balloon! Looks awesome to me. We all love hot air balloons, don't we? Except for the people who have acrophobia and globophobia.

Ooh, look at that Jack Daniels balloon! Looks awesome to me.
We all love hot air balloons, don’t we? Except for the people who have acrophobia and globophobia.

Why does the balloon expand?

The temperature of a gas is a measure of the speed of its molecules. Increasing the temperature of a gas increases the average speed (and therefore the kinetic energy) of the molecules. This causes the molecules to ‘spread out’ – a phenomenon called thermal expansion.

Initially, the gas (air) molecules inside and outside the bottle are at the same temperature and therefore moving at the same speed. Air molecules collide into the balloon with the same energy inside and outside the balloon.

When the balloon is heated, the air molecules inside start moving aster. These molecules now collide into the balloon with more energy resulting in increased pressure. The increased pressure causes the balloon to expand.

Why does hot air rise?

Hot air is less dense than cold air. Any substance that is less dense than the fluid (gas or liquid) of its surroundings will float. So, just as wood floats because it is less than water, hot air floats on cold air because it is less dense. This is how hot air balloons get their lift.

But wait… that leads to another question: why is hot air less dense?

When you heat a material, the particles start to move around more (kinetic molecular theory). In the case of a gas, this means that the particles will be more likely to move apart, which causes the density to decrease. Due to buoyancy, which is the property that materials will float in a less dense substance. So a hot air balloon, as I wrote above, is full of air that is less dense than the air around it, and the mass of the balloon itself is sufficiently overcome by a buoyant force (because it holds a large volume), so the balloon floats.

Then how does helium rise? Helium isn’t hot!

However, a helium balloon floats without heat because the helium is lighter (He is lighter than the different elements and compounds in air), and thus it is less dense. And, I think you learnt the Archimedes Principle in high school – yes, this is it. The balloon displaces a volume of air equal to its volume, and experiences a buoyant force equal to the weight of that much air.
If the balloon is full of air, that buoyant force is less that the weight of the balloon. It would fall.
If the balloon is full of helium, that buoyant force is more than the weight of the balloon itself. It lifts.
So it is indeed because helium is lighter than air, i.e., because the volume of helium displaces more than its weight in air.

See! You just used a physics principle in understanding something. That’s what I love about physics. Keeping mathematicians aside, in mathematics, you learn algebra in high school but never use it later in life. You can use physics in every second of your life (I think I’m going to quote myself :’))
But hey, I love mathematics. I’m not conspiring against it.

So there, I answered that question in just… 600 words. Seems a bit brief, doesn’t it? Well, I can explain more.

Explaining more properly

So, hot air is lighter than cool air, because it has less mass per unit of volume. A cubic foot of air weighs roughly 28 grams (about an ounce). If you heat that air by 100 degrees F, it weighs about 7 grams less. Therefore, each cubic foot of air contained in a hot air balloon can lift about 7 grams. That’s not much, and this is why hot air balloons are so huge — to lift 1,000 pounds, you need about 65,000 cubic feet of hot air.

So, if hot air rises, how fast does it rise?

Now we’re getting into assumptions and stuff. To know how fast hot air rises, we would need to know the type of gas, how hot it is, elevation above sea level, whether it is rising in a tube or in the open, and the volume of hot gas. As you increase the temperature and/or amount it will rise faster without dissipating.

I don’t think I have an equation for that to attach but I think this is natural convection. Explain? Explain.

Natural convection

In natural convection, the fluid motion occurs by natural means such as buoyancy (which I just talked about). Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient encountered in natural convection is also low.

Mechanisms of natural convection

Consider a hot object exposed to cold air. The temperature of the outside of the object will drop (as a result of heat transfer with cold air), and the temperature of adjacent air to the object will rise. Consequently, the object is surrounded with a thin layer of warmer air and heat will be transferred from this layer to the outer layers of air.

In a gravitational field, there is a net force that pushed a light fluid placed in a heavier fluid upwards. This force is called the buoyancy force.

There is a lot more to write about natural convection – Grashof number, Rayleigh number, and all. But I don’t think I should write that under this topic. And, we have shifted our site to this link now. I know it is/was a pain in the arse to change everything, we’re sorry. 😥

Comment below if you have any questions related to science or our new theme and site.

References & Resources

  1. Slider and content image via Travel Blat. Retrieved from:
    http://goo.gl/0MQuj
  2. Physics Forums
  3. Wikipedia – Natural convection
  4. M. Bahrami. Simon Fraser University: Natural Convection.
  5. Tom Harris. HowStuffWorks: How Hot Air Balloons Work. Retrieved from:
    http://goo.gl/bXWXN
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