Heating Air Makes It Lighter Without Removing Any of It
Learn why an object floats by comparing it with the water it displaces, calculate density from mass and volume, predict floating or sinking from density alone, and see how heat and pressure change density.
How can heating air make it lighter without taking any away?
By spreading the same air over a larger volume. Heating makes the particles move faster and push further apart, so each cubic metre now contains fewer of them — and that means a lower density.
Nothing was removed; the air simply became less tightly packed. This page covers everything in the CBSE Class 8 Science chapter's second part: floating and displaced water, calculating density, predicting floating, and how temperature and pressure change density.
Nothing was removed; the air simply became less tightly packed. This page covers everything in the CBSE Class 8 Science chapter's second part: floating and displaced water, calculating density, predicting floating, and how temperature and pressure change density.
Why does an object float by comparing it with the water it displaces?
Because an object pushes aside — displaces — some water when placed in it, and what happens next depends on how the object's weight compares with the weight of that displaced water.
- If the object is lighter than the water it displaces, it floats.
- If it is heavier than the water it displaces, it sinks.
That is why the comparison must always be between equal volumes. A large log floats while a small iron nail sinks, even though the log is far heavier overall — because for the same volume, wood weighs less than water and iron weighs more.
Try it with a lump of clay. Rolled into a ball it sinks, because it displaces only a little water. Flatten the same clay into a bowl shape and it floats, because the hollow shape displaces far more water while the clay's weight has not changed at all.
That clay experiment is the answer to how an iron ship floats. Its hull encloses a great deal of air, so the ship displaces an enormous volume of water — enough to outweigh the ship itself. Let water into the hull and the displaced volume no longer outweighs it, which is what sinking means.
So the useful question is never "how heavy is it?" but how heavy is it for its volume — and that quantity has a name, which the next section defines.
- If the object is lighter than the water it displaces, it floats.
- If it is heavier than the water it displaces, it sinks.
That is why the comparison must always be between equal volumes. A large log floats while a small iron nail sinks, even though the log is far heavier overall — because for the same volume, wood weighs less than water and iron weighs more.
Try it with a lump of clay. Rolled into a ball it sinks, because it displaces only a little water. Flatten the same clay into a bowl shape and it floats, because the hollow shape displaces far more water while the clay's weight has not changed at all.
That clay experiment is the answer to how an iron ship floats. Its hull encloses a great deal of air, so the ship displaces an enormous volume of water — enough to outweigh the ship itself. Let water into the hull and the displaced volume no longer outweighs it, which is what sinking means.
So the useful question is never "how heavy is it?" but how heavy is it for its volume — and that quantity has a name, which the next section defines.
Formula
How do you calculate density?
Density is the mass per unit volume of a substance:
Its units are grams per cubic centimetre () or kilograms per cubic metre (), and
Worked examples.
A metal block of mass occupying :
which in SI units is .
A block of wood of mass and volume :
An irregular metal piece of mass that raises the water in a measuring cylinder from to , so its volume is :
which identifies it as iron.
Water is the reference: its density is , or . So one litre of water has a mass of exactly .
Density belongs to the substance, not to the piece, and that is the point often missed. Cutting an iron bar in half halves both the mass and the volume, so the ratio is unchanged — every iron filing has the density of iron.
Its units are grams per cubic centimetre () or kilograms per cubic metre (), and
Worked examples.
A metal block of mass occupying :
which in SI units is .
A block of wood of mass and volume :
An irregular metal piece of mass that raises the water in a measuring cylinder from to , so its volume is :
which identifies it as iron.
Water is the reference: its density is , or . So one litre of water has a mass of exactly .
Density belongs to the substance, not to the piece, and that is the point often missed. Cutting an iron bar in half halves both the mass and the volume, so the ratio is unchanged — every iron filing has the density of iron.
How do you predict whether something floats or sinks?
Compare its density with the density of water, .
- Density less than — it floats
- Density greater than — it sinks
- Density equal to — it stays wherever it is placed, fully submerged
Applying it:
- Cork, about — floats, and rides high
- Wood, about — floats
- Ice, — floats, with most of it below the surface
- Oil, about — floats on water, which is why it forms a layer on top
- Iron, — sinks
- Stone, glass marble, coin — all denser than water, so all sink
The wooden block calculated in the last section, at , floats; the iron piece at sinks. The prediction needed no experiment at all.
Ice floating has consequences beyond the classroom: because solid water is less dense than liquid water, ice forms a layer on top of a pond rather than sinking, and the water beneath stays liquid enough for fish to survive.
Floating is a property of the pair, not of the object alone. An egg that sinks in plain water floats in strongly salted water, because salt water is denser — the egg has not changed, only the liquid has.
- Density less than — it floats
- Density greater than — it sinks
- Density equal to — it stays wherever it is placed, fully submerged
Applying it:
- Cork, about — floats, and rides high
- Wood, about — floats
- Ice, — floats, with most of it below the surface
- Oil, about — floats on water, which is why it forms a layer on top
- Iron, — sinks
- Stone, glass marble, coin — all denser than water, so all sink
The wooden block calculated in the last section, at , floats; the iron piece at sinks. The prediction needed no experiment at all.
Ice floating has consequences beyond the classroom: because solid water is less dense than liquid water, ice forms a layer on top of a pond rather than sinking, and the water beneath stays liquid enough for fish to survive.
Floating is a property of the pair, not of the object alone. An egg that sinks in plain water floats in strongly salted water, because salt water is denser — the egg has not changed, only the liquid has.
How do temperature and pressure change density?
Both change the volume while leaving the mass alone, so both change the density.
Heating makes particles move faster and spread further apart. The same mass now occupies a larger volume, so the density decreases.
Cooling brings the particles closer, so the volume shrinks and the density increases.
Increasing pressure squeezes a substance into a smaller volume, so the density increases — an effect large for gases, very small for liquids, and negligible for solids, exactly as their compressibilities differ.
The consequences are everywhere:
- Hot air rises. Air warmed by a stove or a fire becomes less dense than the cooler air around it, so it floats upward and cooler air moves in below. This is the convection current that drives a room's air, a sea breeze and the monsoon.
- A hot air balloon rises because the air inside it is heated and made less dense than the surrounding air.
- Ventilators are placed near the ceiling, because hot used air collects at the top.
- Smoke from a chimney climbs, being hot and therefore less dense than the air outside.
- LPG is stored as a liquid because enormous pressure has squeezed the gas into a far denser form.
Water has a famous exception worth remembering: between and it contracts on heating rather than expanding, which is why ice is less dense than the water beneath it.
What must not slip is that the mass never changes. Heating air does not remove any of it — the same particles simply occupy more room, so the density falls while the mass stays exactly the same, which is precisely why hot air rises rather than disappearing.
Heating makes particles move faster and spread further apart. The same mass now occupies a larger volume, so the density decreases.
Cooling brings the particles closer, so the volume shrinks and the density increases.
Increasing pressure squeezes a substance into a smaller volume, so the density increases — an effect large for gases, very small for liquids, and negligible for solids, exactly as their compressibilities differ.
The consequences are everywhere:
- Hot air rises. Air warmed by a stove or a fire becomes less dense than the cooler air around it, so it floats upward and cooler air moves in below. This is the convection current that drives a room's air, a sea breeze and the monsoon.
- A hot air balloon rises because the air inside it is heated and made less dense than the surrounding air.
- Ventilators are placed near the ceiling, because hot used air collects at the top.
- Smoke from a chimney climbs, being hot and therefore less dense than the air outside.
- LPG is stored as a liquid because enormous pressure has squeezed the gas into a far denser form.
Water has a famous exception worth remembering: between and it contracts on heating rather than expanding, which is why ice is less dense than the water beneath it.
What must not slip is that the mass never changes. Heating air does not remove any of it — the same particles simply occupy more room, so the density falls while the mass stays exactly the same, which is precisely why hot air rises rather than disappearing.
Exam tip
Exam tip: keeping the units consistent before dividing
Density numericals are short, and nearly every lost mark is a unit.
Bring mass and volume into one system before dividing — grams with cubic centimetres gives , kilograms with cubic metres gives . Grams divided by cubic metres means nothing.
Remember the one conversion: , so is .
Write the formula first, then substitute, then attach the unit to the answer.
For floating questions, compare against water's and state the comparison: *density is less than , so it floats.*
And when explaining hot air rising, say that the volume increases while the mass stays the same, so the density falls. Saying "hot air is lighter" without that reasoning earns only part of the mark.
Bring mass and volume into one system before dividing — grams with cubic centimetres gives , kilograms with cubic metres gives . Grams divided by cubic metres means nothing.
Remember the one conversion: , so is .
Write the formula first, then substitute, then attach the unit to the answer.
For floating questions, compare against water's and state the comparison: *density is less than , so it floats.*
And when explaining hot air rising, say that the volume increases while the mass stays the same, so the density falls. Saying "hot air is lighter" without that reasoning earns only part of the mark.
Did you know
Why does the same lump of clay sink as a ball but float as a bowl?
Because changing its shape changes how much water it pushes aside.
Rolled into a tight ball, the clay displaces only its own small volume of water — far less water than the clay weighs, so it sinks. Pressed into a wide, hollow bowl, the same clay encloses a large space, so it displaces a much greater volume of water.
The clay's mass is identical in both cases. What changed is the volume of water displaced, and once that displaced water outweighs the clay, it floats. That is the whole principle behind a steel ship, and why letting water into the hollow part sinks it.
Rolled into a tight ball, the clay displaces only its own small volume of water — far less water than the clay weighs, so it sinks. Pressed into a wide, hollow bowl, the same clay encloses a large space, so it displaces a much greater volume of water.
The clay's mass is identical in both cases. What changed is the volume of water displaced, and once that displaced water outweighs the clay, it floats. That is the whole principle behind a steel ship, and why letting water into the hollow part sinks it.
Key takeaways
Density, floating and hot air: quick revision
- An object floats if it is lighter than the water it displaces and sinks if heavier — which is why the same clay sinks as a ball and floats as a bowl.
- , in or , with .
- Water's density is , so one litre has a mass of ; a block of volume has density .
- Density belongs to the substance, not the piece — cutting it in half changes nothing.
- Density below floats (cork, wood, ice, oil), above it sinks (iron, stone, glass) — and the same egg floats in salt water but sinks in plain.
- Heating lowers density and pressure raises it, because only the volume changes while the mass stays the same — which is why hot air rises, balloons lift and ventilators sit near the ceiling.
You will remember all of this far better after answering five questions on it than after reading it twice.
- , in or , with .
- Water's density is , so one litre has a mass of ; a block of volume has density .
- Density belongs to the substance, not the piece — cutting it in half changes nothing.
- Density below floats (cork, wood, ice, oil), above it sinks (iron, stone, glass) — and the same egg floats in salt water but sinks in plain.
- Heating lowers density and pressure raises it, because only the volume changes while the mass stays the same — which is why hot air rises, balloons lift and ventilators sit near the ceiling.
You will remember all of this far better after answering five questions on it than after reading it twice.