A Straight Line That Hits Zero Volume at Minus 273 Degrees
Explain gas behaviour by molecular motion, solve pressure-volume problems with Boyle's Law and volume-temperature problems with Charles's Law, and see where absolute zero comes from.
Why does squeezing a gas raise its pressure but squeezing water does nothing?
Block the outlet of a bicycle pump with your thumb and push the handle. It goes in a long way, and the harder you push the harder it pushes back.
Now try the same thing with a syringe full of water. The plunger will not move at all.
Both are fluids and both are made of molecules, so why does one compress easily and the other not at all?
Because in a gas the molecules are far apart. There is a great deal of empty space between them, and squeezing the gas mostly squeezes that space. In water the molecules are already touching, so there is nothing left to squeeze out.
That single difference — large inter-particle space in a gas — is what makes the behaviour of gases simple enough to capture in two short laws. Pressure and volume are inversely related, and volume and temperature are directly related, and between them those two statements answer most of the questions in this chapter.
There is also a surprise waiting at the end of the second law. Extend its straight-line graph backwards and it predicts a temperature at which a gas would have no volume at all — which turns out to be the coldest temperature there can be.
This page covers the first part of the ICSE Class 9 Chemistry chapter on gas laws: the molecular explanation, Boyle's Law with graphs and numericals, Charles's Law with graphs and numericals, and absolute zero with the Kelvin scale.
Now try the same thing with a syringe full of water. The plunger will not move at all.
Both are fluids and both are made of molecules, so why does one compress easily and the other not at all?
Because in a gas the molecules are far apart. There is a great deal of empty space between them, and squeezing the gas mostly squeezes that space. In water the molecules are already touching, so there is nothing left to squeeze out.
That single difference — large inter-particle space in a gas — is what makes the behaviour of gases simple enough to capture in two short laws. Pressure and volume are inversely related, and volume and temperature are directly related, and between them those two statements answer most of the questions in this chapter.
There is also a surprise waiting at the end of the second law. Extend its straight-line graph backwards and it predicts a temperature at which a gas would have no volume at all — which turns out to be the coldest temperature there can be.
This page covers the first part of the ICSE Class 9 Chemistry chapter on gas laws: the molecular explanation, Boyle's Law with graphs and numericals, Charles's Law with graphs and numericals, and absolute zero with the Kelvin scale.
What happens to gas molecules when you heat or squeeze them?
A gas consists of molecules in rapid random motion, separated by inter-particle spaces that are very large compared with the molecules themselves, with almost no forces of attraction between them.
Everything a gas does follows from those three facts.
Where pressure comes from. The molecules are constantly striking the walls of the container. Each collision gives the wall a tiny push, and the combined effect of an enormous number of collisions every second is what we measure as pressure. So pressure depends on how hard the molecules hit and how often they hit.
What heating does. Raising the temperature makes the molecules move faster. Faster molecules strike the walls harder and more frequently. So:
- If the volume is fixed, the pressure rises
- If the pressure is fixed — a container that can expand — the gas expands until the collisions are spread over a larger area again
A pressure cooker on a stove is the first case: the volume cannot change, so the pressure climbs until the weight lifts. A balloon left in a hot room is the second: it stretches until the inside and outside pressures match again.
What squeezing does. Reducing the volume puts the same number of molecules into a smaller space. Each molecule now has less distance to travel between collisions with the wall, so the number of collisions per unit area each second goes up — and the pressure rises.
Why gases are so compressible and liquids are not. In a gas the inter-particle space is very much larger than the molecules, so there is a great deal of emptiness to remove. In a liquid or a solid the particles are already close together with strong forces between them, so almost nothing can be removed. A gas can be squeezed to a small fraction of its volume; water cannot be squeezed measurably at all.
Cooling a balloon makes this visible. Dip an inflated balloon into cold water and it shrinks; take it out and it recovers. The number of molecules inside has not changed by one — they have only slowed down, so they push less hard, and the outside air pressure pushes the skin inwards until the two balance.
Notice that the molecules themselves are never described as expanding or contracting. A common mistake is to say that a gas expands on heating because its molecules get bigger. They do not. The molecules keep exactly the same size and only change their speed, and it is the space between them that changes — which is why the same reasoning explains a rise in pressure at fixed volume and an increase in volume at fixed pressure.
Everything a gas does follows from those three facts.
Where pressure comes from. The molecules are constantly striking the walls of the container. Each collision gives the wall a tiny push, and the combined effect of an enormous number of collisions every second is what we measure as pressure. So pressure depends on how hard the molecules hit and how often they hit.
What heating does. Raising the temperature makes the molecules move faster. Faster molecules strike the walls harder and more frequently. So:
- If the volume is fixed, the pressure rises
- If the pressure is fixed — a container that can expand — the gas expands until the collisions are spread over a larger area again
A pressure cooker on a stove is the first case: the volume cannot change, so the pressure climbs until the weight lifts. A balloon left in a hot room is the second: it stretches until the inside and outside pressures match again.
What squeezing does. Reducing the volume puts the same number of molecules into a smaller space. Each molecule now has less distance to travel between collisions with the wall, so the number of collisions per unit area each second goes up — and the pressure rises.
Why gases are so compressible and liquids are not. In a gas the inter-particle space is very much larger than the molecules, so there is a great deal of emptiness to remove. In a liquid or a solid the particles are already close together with strong forces between them, so almost nothing can be removed. A gas can be squeezed to a small fraction of its volume; water cannot be squeezed measurably at all.
Cooling a balloon makes this visible. Dip an inflated balloon into cold water and it shrinks; take it out and it recovers. The number of molecules inside has not changed by one — they have only slowed down, so they push less hard, and the outside air pressure pushes the skin inwards until the two balance.
Notice that the molecules themselves are never described as expanding or contracting. A common mistake is to say that a gas expands on heating because its molecules get bigger. They do not. The molecules keep exactly the same size and only change their speed, and it is the space between them that changes — which is why the same reasoning explains a rise in pressure at fixed volume and an increase in volume at fixed pressure.
Formula
How do you solve a pressure and volume problem with Boyle's Law?
Boyle's Law: at constant temperature, the volume of a given mass of a gas is inversely proportional to its pressure.
So the product of pressure and volume is a constant, which gives the working form:
Two conditions are attached to the law and both must be quoted. The temperature must be constant, and the mass of gas must be fixed — no gas added or allowed to escape.
Worked example 1. A gas occupies at a pressure of of mercury. What volume will it occupy at , the temperature staying the same?
The pressure was increased by half again, and the volume fell to two-thirds. A rise in pressure must give a fall in volume, so if your answer comes out larger you have inverted the fraction.
Worked example 2. of a gas at is compressed to at the same temperature. Find the new pressure.
The volume was quartered and the pressure became four times as great — exactly what inverse proportion requires.
The graphs, all three of which are examinable.
- ** against — a smooth curve falling away from both axes, called a rectangular hyperbola. It never touches either axis, because neither the pressure nor the volume can become zero
- against — a straight line through the origin**, because is directly proportional to
- ** against — a horizontal straight line**, because the product does not change at all
The straight-line graph is the useful one, and it is worth knowing why. A curve is hard to check by eye; a straight line through the origin is easy. So plotting against rather than against converts the law into the one shape you can verify at a glance. Turning a curved relationship into a straight line by plotting a reciprocal is a standard experimental trick, and it is the reason this particular graph appears in every question on the topic.
The units do not have to be SI, but they must match. If is in cubic centimetres then comes out in cubic centimetres; if is in millimetres of mercury then is too. Since the same quantity appears on both sides, the units cancel — so a problem mixing litres with cubic centimetres needs one conversion before you start, and that is the commonest source of a wrong answer in Boyle's Law sums.
So the product of pressure and volume is a constant, which gives the working form:
Two conditions are attached to the law and both must be quoted. The temperature must be constant, and the mass of gas must be fixed — no gas added or allowed to escape.
Worked example 1. A gas occupies at a pressure of of mercury. What volume will it occupy at , the temperature staying the same?
The pressure was increased by half again, and the volume fell to two-thirds. A rise in pressure must give a fall in volume, so if your answer comes out larger you have inverted the fraction.
Worked example 2. of a gas at is compressed to at the same temperature. Find the new pressure.
The volume was quartered and the pressure became four times as great — exactly what inverse proportion requires.
The graphs, all three of which are examinable.
- ** against — a smooth curve falling away from both axes, called a rectangular hyperbola. It never touches either axis, because neither the pressure nor the volume can become zero
- against — a straight line through the origin**, because is directly proportional to
- ** against — a horizontal straight line**, because the product does not change at all
The straight-line graph is the useful one, and it is worth knowing why. A curve is hard to check by eye; a straight line through the origin is easy. So plotting against rather than against converts the law into the one shape you can verify at a glance. Turning a curved relationship into a straight line by plotting a reciprocal is a standard experimental trick, and it is the reason this particular graph appears in every question on the topic.
The units do not have to be SI, but they must match. If is in cubic centimetres then comes out in cubic centimetres; if is in millimetres of mercury then is too. Since the same quantity appears on both sides, the units cancel — so a problem mixing litres with cubic centimetres needs one conversion before you start, and that is the commonest source of a wrong answer in Boyle's Law sums.
How do you solve a volume and temperature problem with Charles's Law?
Charles's Law: at constant pressure, the volume of a given mass of a gas is directly proportional to its absolute temperature.
So the ratio of volume to temperature is a constant, giving the working form:
The word "absolute" is doing essential work there. must be in kelvin, never in degrees Celsius, and the next section explains why.
Worked example 1. A gas occupies at . What volume will it occupy at , the pressure staying the same?
Convert both temperatures first:
The gas was heated, so it expanded. Heating must increase the volume, and an answer smaller than the original means the fraction was inverted.
Worked example 2. of a gas at is cooled to at constant pressure. Find the new volume.
The absolute temperature fell to two-thirds of its value, and so did the volume.
Why Celsius cannot be used, shown by doing it wrongly. Repeat example 2 in Celsius and you would write , which is negative — a gas with a negative volume. The arithmetic is not merely inaccurate; it is meaningless. Direct proportion requires a scale whose zero is a genuine zero of the quantity, and is not a temperature at which anything stops. The Kelvin scale has that property and the Celsius scale does not.
The graphs.
- ** against in kelvin — a straight line passing through the origin, since the two are directly proportional
- against in degrees Celsius — a straight line** of the same slope, but it does not pass through the origin. Extended backwards it cuts the temperature axis at
That intercept is the whole reason the next section exists. The Celsius graph is the same physical line, merely labelled with a scale whose zero sits in the wrong place, and where it crosses the axis is the point at which the scale should have started.
So the ratio of volume to temperature is a constant, giving the working form:
The word "absolute" is doing essential work there. must be in kelvin, never in degrees Celsius, and the next section explains why.
Worked example 1. A gas occupies at . What volume will it occupy at , the pressure staying the same?
Convert both temperatures first:
The gas was heated, so it expanded. Heating must increase the volume, and an answer smaller than the original means the fraction was inverted.
Worked example 2. of a gas at is cooled to at constant pressure. Find the new volume.
The absolute temperature fell to two-thirds of its value, and so did the volume.
Why Celsius cannot be used, shown by doing it wrongly. Repeat example 2 in Celsius and you would write , which is negative — a gas with a negative volume. The arithmetic is not merely inaccurate; it is meaningless. Direct proportion requires a scale whose zero is a genuine zero of the quantity, and is not a temperature at which anything stops. The Kelvin scale has that property and the Celsius scale does not.
The graphs.
- ** against in kelvin — a straight line passing through the origin, since the two are directly proportional
- against in degrees Celsius — a straight line** of the same slope, but it does not pass through the origin. Extended backwards it cuts the temperature axis at
That intercept is the whole reason the next section exists. The Celsius graph is the same physical line, merely labelled with a scale whose zero sits in the wrong place, and where it crosses the axis is the point at which the scale should have started.
Where does absolute zero come from, and how do you convert temperatures?
**Absolute zero is the temperature at which the volume of a gas would become zero — — and it is the lowest temperature there can be.
Where the number comes from.** Charles's Law can also be stated in this form: at constant pressure, a given mass of gas expands or contracts by of its volume at for each degree Celsius of temperature change. So the volume at is:
Now put :
The volume comes out as zero. Cooling further would make it negative, which is impossible — so no temperature below can exist. That temperature is absolute zero, and it is taken as the zero of the Kelvin scale.
The conversion, which you will use in every numerical from here on.
Worked conversions.
- — the ice point
- — ordinary room temperature, and the value that appears in most problems
- — the steam point
-
- — absolute zero
-
-
A degree on the two scales is the same size. Only the zero has moved. So a temperature difference of is also a difference of , and you never multiply or divide when converting — you only add or subtract .
One important qualification. No real gas actually reaches zero volume, because every gas liquefies well before is reached, and Charles's Law stops applying once it is no longer a gas. The zero volume is obtained by extending the straight-line graph beyond the region where the gas exists.
So absolute zero is defined by an extrapolation rather than observed directly, and that is the honest answer to a question asking whether a gas can be cooled to zero volume. It cannot — but the line still tells you where the temperature scale ought to begin, and every gas, whatever it is, gives a line pointing at the same . That agreement between different gases is what makes the temperature a property of nature rather than of the gas being tested.
Where the number comes from.** Charles's Law can also be stated in this form: at constant pressure, a given mass of gas expands or contracts by of its volume at for each degree Celsius of temperature change. So the volume at is:
Now put :
The volume comes out as zero. Cooling further would make it negative, which is impossible — so no temperature below can exist. That temperature is absolute zero, and it is taken as the zero of the Kelvin scale.
The conversion, which you will use in every numerical from here on.
Worked conversions.
- — the ice point
- — ordinary room temperature, and the value that appears in most problems
- — the steam point
-
- — absolute zero
-
-
A degree on the two scales is the same size. Only the zero has moved. So a temperature difference of is also a difference of , and you never multiply or divide when converting — you only add or subtract .
One important qualification. No real gas actually reaches zero volume, because every gas liquefies well before is reached, and Charles's Law stops applying once it is no longer a gas. The zero volume is obtained by extending the straight-line graph beyond the region where the gas exists.
So absolute zero is defined by an extrapolation rather than observed directly, and that is the honest answer to a question asking whether a gas can be cooled to zero volume. It cannot — but the line still tells you where the temperature scale ought to begin, and every gas, whatever it is, gives a line pointing at the same . That agreement between different gases is what makes the temperature a property of nature rather than of the gas being tested.
Exam tip
Exam tip: convert to kelvin before you write anything else
Convert every temperature to kelvin first, at the top of your working, before substituting. .
State both conditions with each law. Boyle's Law holds at constant temperature for a given mass of gas; Charles's Law at constant pressure for a given mass of gas. Dropping the condition loses the mark.
**Boyle: . Charles: . Write the equation before substituting numbers.
Check the direction of your answer. More pressure means less volume; more temperature means more volume. A wrong direction means an inverted fraction, and it is the fastest error to catch.
Make the units match. Litres with litres, cubic centimetres with cubic centimetres. Convert once, at the start.
Learn all three Boyle graphs**: against is a rectangular hyperbola; against is a straight line through the origin; against is a horizontal line.
Learn both Charles graphs: against in kelvin passes through the origin; against in Celsius cuts the axis at .
Derive absolute zero when asked — substitute into and show that the volume becomes zero.
Say that no gas reaches it, because every gas liquefies first — the value comes from extending the graph.
And never say that molecules expand on heating. They move faster; the space between them changes.
State both conditions with each law. Boyle's Law holds at constant temperature for a given mass of gas; Charles's Law at constant pressure for a given mass of gas. Dropping the condition loses the mark.
**Boyle: . Charles: . Write the equation before substituting numbers.
Check the direction of your answer. More pressure means less volume; more temperature means more volume. A wrong direction means an inverted fraction, and it is the fastest error to catch.
Make the units match. Litres with litres, cubic centimetres with cubic centimetres. Convert once, at the start.
Learn all three Boyle graphs**: against is a rectangular hyperbola; against is a straight line through the origin; against is a horizontal line.
Learn both Charles graphs: against in kelvin passes through the origin; against in Celsius cuts the axis at .
Derive absolute zero when asked — substitute into and show that the volume becomes zero.
Say that no gas reaches it, because every gas liquefies first — the value comes from extending the graph.
And never say that molecules expand on heating. They move faster; the space between them changes.
Did you know
Why two different gases point at exactly the same temperature
Take a fixed mass of hydrogen at constant pressure, measure its volume at several temperatures and plot the points. You get a straight line. Extend it backwards beyond the measurements and it crosses the temperature axis at about minus two hundred and seventy-three degrees Celsius.
Now do it again with oxygen. Different gas, different molecules, different mass, different volume — and a different line, with a different slope.
It crosses the axis at the same place.
Do it with nitrogen, with helium, with carbon dioxide. Every line has its own slope, and every line points at the same intercept.
That agreement is the most interesting thing in this chapter, and it is easy to read past. If the intercept had come out differently for each gas, it would simply have been a fact about that gas — a quirk of hydrogen, say, with no wider meaning. But a value that every gas agrees on cannot be a property of any one of them. It has to be a property of temperature itself.
That is what justifies building a whole new temperature scale on it. The Celsius scale was fixed by two convenient reference points, the melting of ice and the boiling of water, and there is nothing fundamental about either — they are properties of one particular substance. The zero of the Kelvin scale is not chosen. It is the point every gas independently identifies as the place where the line runs out.
And notice that no gas is ever actually at that temperature during the experiment. Each one liquefies long before, so the crossing point lies entirely outside the range where any measurement was possible. The lines are agreeing about a place none of them can visit.
A measurement that several unrelated systems agree on, in a region where none of them can be tested, is usually a sign that you have found something real — which is why absolute zero is taken as a genuine physical limit rather than an artefact of drawing straight lines too far.
Now do it again with oxygen. Different gas, different molecules, different mass, different volume — and a different line, with a different slope.
It crosses the axis at the same place.
Do it with nitrogen, with helium, with carbon dioxide. Every line has its own slope, and every line points at the same intercept.
That agreement is the most interesting thing in this chapter, and it is easy to read past. If the intercept had come out differently for each gas, it would simply have been a fact about that gas — a quirk of hydrogen, say, with no wider meaning. But a value that every gas agrees on cannot be a property of any one of them. It has to be a property of temperature itself.
That is what justifies building a whole new temperature scale on it. The Celsius scale was fixed by two convenient reference points, the melting of ice and the boiling of water, and there is nothing fundamental about either — they are properties of one particular substance. The zero of the Kelvin scale is not chosen. It is the point every gas independently identifies as the place where the line runs out.
And notice that no gas is ever actually at that temperature during the experiment. Each one liquefies long before, so the crossing point lies entirely outside the range where any measurement was possible. The lines are agreeing about a place none of them can visit.
A measurement that several unrelated systems agree on, in a region where none of them can be tested, is usually a sign that you have found something real — which is why absolute zero is taken as a genuine physical limit rather than an artefact of drawing straight lines too far.
Exam relevance
How are the gas laws tested in JEE Main and NEET?
Because they combine into one equation that every later chapter on gases uses, and that equation is a reliable source of numericals.
This is the foundation for Class 11 Chemistry States of Matter and Class 11 Physics Kinetic Theory and Thermal Properties of Matter, examined in both JEE Main and NEET. Boyle's Law and Charles's Law are combined with Avogadro's Law into the ideal gas equation , and the two-state forms used here become the single most-used equation in physical chemistry.
The molecular picture becomes the kinetic theory of gases. Class 11 derives pressure from molecular collisions properly, giving , and defines the root mean square, average and most probable speeds. The qualitative statement here — pressure comes from how hard and how often the molecules strike the wall — is exactly what that derivation makes quantitative, and questions on the relation between temperature and molecular speed follow directly.
Deviations from the laws become a topic of their own. Class 11 explains why real gases disobey Boyle's Law at high pressure and low temperature, introduces the compressibility factor and the van der Waals equation with its corrections for molecular volume and intermolecular attraction. Those two corrections are precisely the two assumptions made on this page — negligible molecular volume and negligible forces — so knowing which assumption fails tells you which correction applies. Assertion-reason questions on real-gas behaviour are a recurring JEE Main type.
Absolute zero and the Kelvin scale carry into thermodynamics. Class 11 Thermodynamics uses kelvin throughout, and the third law concerns the unattainability of absolute zero. The extrapolation argument given here is the elementary version of that idea.
Graph interpretation is examined directly. Both JEE Main and NEET set questions showing a -against- or -against- graph and asking which law or which constant condition it represents, or which of several plotted lines corresponds to the higher temperature. Isotherms, isobars and isochores are named in Class 11, and each is one of the graphs drawn on this page.
For NEET Physics, the gas laws appear in kinetic theory as numericals on pressure, temperature and molecular speed. For NEET Biology the same relationships underlie Breathing and Exchange of Gases — the pressure-volume changes of inspiration and expiration are Boyle's Law applied to the chest cavity, and questions on the mechanism of breathing expect that connection.
What the questions look like. For board work, expect state Boyle's Law and Charles's Law with their conditions, sketch the graphical representation, solve for an unknown pressure, volume or temperature, convert between Celsius and kelvin, and **define absolute zero and show where comes from. Numericals need the kelvin conversion shown. For JEE Main and NEET, expect ideal-gas calculations, kinetic-theory numericals, compressibility and graph identification.
How board and competitive emphasis differ. A board paper rewards the stated law with its condition and a clean two-state calculation. A competitive paper assumes both and asks about deviations, molecular speeds or which curve is the higher isotherm.
The single trap that costs the most marks. Substituting degrees Celsius into Charles's Law. The law is a direct proportion** and needs a scale whose zero is a real zero — substituting Celsius can even produce a negative volume, as cooling to demonstrates. **The defence is mechanical: write and in kelvin on their own line before you touch the formula**, so the conversion cannot be skipped under time pressure.
This is the foundation for Class 11 Chemistry States of Matter and Class 11 Physics Kinetic Theory and Thermal Properties of Matter, examined in both JEE Main and NEET. Boyle's Law and Charles's Law are combined with Avogadro's Law into the ideal gas equation , and the two-state forms used here become the single most-used equation in physical chemistry.
The molecular picture becomes the kinetic theory of gases. Class 11 derives pressure from molecular collisions properly, giving , and defines the root mean square, average and most probable speeds. The qualitative statement here — pressure comes from how hard and how often the molecules strike the wall — is exactly what that derivation makes quantitative, and questions on the relation between temperature and molecular speed follow directly.
Deviations from the laws become a topic of their own. Class 11 explains why real gases disobey Boyle's Law at high pressure and low temperature, introduces the compressibility factor and the van der Waals equation with its corrections for molecular volume and intermolecular attraction. Those two corrections are precisely the two assumptions made on this page — negligible molecular volume and negligible forces — so knowing which assumption fails tells you which correction applies. Assertion-reason questions on real-gas behaviour are a recurring JEE Main type.
Absolute zero and the Kelvin scale carry into thermodynamics. Class 11 Thermodynamics uses kelvin throughout, and the third law concerns the unattainability of absolute zero. The extrapolation argument given here is the elementary version of that idea.
Graph interpretation is examined directly. Both JEE Main and NEET set questions showing a -against- or -against- graph and asking which law or which constant condition it represents, or which of several plotted lines corresponds to the higher temperature. Isotherms, isobars and isochores are named in Class 11, and each is one of the graphs drawn on this page.
For NEET Physics, the gas laws appear in kinetic theory as numericals on pressure, temperature and molecular speed. For NEET Biology the same relationships underlie Breathing and Exchange of Gases — the pressure-volume changes of inspiration and expiration are Boyle's Law applied to the chest cavity, and questions on the mechanism of breathing expect that connection.
What the questions look like. For board work, expect state Boyle's Law and Charles's Law with their conditions, sketch the graphical representation, solve for an unknown pressure, volume or temperature, convert between Celsius and kelvin, and **define absolute zero and show where comes from. Numericals need the kelvin conversion shown. For JEE Main and NEET, expect ideal-gas calculations, kinetic-theory numericals, compressibility and graph identification.
How board and competitive emphasis differ. A board paper rewards the stated law with its condition and a clean two-state calculation. A competitive paper assumes both and asks about deviations, molecular speeds or which curve is the higher isotherm.
The single trap that costs the most marks. Substituting degrees Celsius into Charles's Law. The law is a direct proportion** and needs a scale whose zero is a real zero — substituting Celsius can even produce a negative volume, as cooling to demonstrates. **The defence is mechanical: write and in kelvin on their own line before you touch the formula**, so the conversion cannot be skipped under time pressure.
Key takeaways
Boyle's Law, Charles's Law and absolute zero: quick revision
- A gas is molecules in rapid random motion, with inter-particle spaces much larger than the molecules and almost no forces between them.
- Pressure is molecular collisions with the walls — it depends on how hard and how often they strike.
- Heating makes molecules faster: at fixed volume the pressure rises; at fixed pressure the gas expands.
- Squeezing puts the same molecules in less space, so collisions per unit area rise and the pressure rises.
- Gases are highly compressible because there is a great deal of empty space to remove; liquids and solids are not.
- Molecules never change size — only their speed and their spacing change.
- Boyle's Law: at constant temperature, for a given mass of gas, , so is constant and .
- at becomes at .
- at compressed to gives .
- Boyle graphs: against is a rectangular hyperbola; against is a straight line through the origin; against is a horizontal line.
- Charles's Law: at constant pressure, for a given mass of gas, in kelvin, so .
- at becomes at .
- at becomes at .
- Charles graphs: against in kelvin passes through the origin; against in Celsius cuts the axis at .
- Celsius must never be substituted — it can give a negative volume, and direct proportion needs a scale with a true zero.
- Alternative form: — a gas changes by of its volume at per degree.
- Absolute zero: put and . No lower temperature is possible, and it is the zero of the Kelvin scale.
- ****: ; ; ; ; .
- A degree is the same size on both scales, so a temperature difference is the same number in each — only add or subtract, never multiply.
- No gas reaches zero volume — every gas liquefies first, so the value comes from extending the graph, and every gas points at the same intercept.
Take any gas volume at room temperature and work out what it becomes at and at — if the kelvin conversion is automatic, every numerical in the next part becomes a one-line substitution.
- Pressure is molecular collisions with the walls — it depends on how hard and how often they strike.
- Heating makes molecules faster: at fixed volume the pressure rises; at fixed pressure the gas expands.
- Squeezing puts the same molecules in less space, so collisions per unit area rise and the pressure rises.
- Gases are highly compressible because there is a great deal of empty space to remove; liquids and solids are not.
- Molecules never change size — only their speed and their spacing change.
- Boyle's Law: at constant temperature, for a given mass of gas, , so is constant and .
- at becomes at .
- at compressed to gives .
- Boyle graphs: against is a rectangular hyperbola; against is a straight line through the origin; against is a horizontal line.
- Charles's Law: at constant pressure, for a given mass of gas, in kelvin, so .
- at becomes at .
- at becomes at .
- Charles graphs: against in kelvin passes through the origin; against in Celsius cuts the axis at .
- Celsius must never be substituted — it can give a negative volume, and direct proportion needs a scale with a true zero.
- Alternative form: — a gas changes by of its volume at per degree.
- Absolute zero: put and . No lower temperature is possible, and it is the zero of the Kelvin scale.
- ****: ; ; ; ; .
- A degree is the same size on both scales, so a temperature difference is the same number in each — only add or subtract, never multiply.
- No gas reaches zero volume — every gas liquefies first, so the value comes from extending the graph, and every gas points at the same intercept.
Take any gas volume at room temperature and work out what it becomes at and at — if the kelvin conversion is automatic, every numerical in the next part becomes a one-line substitution.