We feel hot when it is hot, we feel cold when it is cold. Temperature can mean different things to different people at different times.
If we think about measuring temperature, we think of the thermometer. It used to be that long glass tube with a red liquid line that grow longer when it is hot, shorter when it is cold.
If we hold a cup of cold water, our hand - at least the skin of our hand - can get as cold as the cup. Actually, the cup of water also gets warmer because of our hand.
So some heat goes from our hand to the water. Or some coldness goes from the water to our hand?
When the water and our hand gets equally cold or equally warm - depending on your point of view, then they have the same temperature. We call this situation "thermal equilbrium". It kind of means that the flow of heat (or coldness?) between the two objects are balanced.
Something that soon becomes obvious to observant people is that things tend to expand a bit when warm, and contract a bit when cold. This likely led to the inventing of the thermometer. Just put some liquid in a narrow glass tube. It gets longer when warm, shorter when cold. Mark out some numbers next to it, and we have a thermometer!
The expansion and contraction is most obvious for a gas, filled in a bag or balloon. People also found that the balloons float when filled with warm air. Hot air balloon has been used to carry people since 200 years ago.
At some point, some scientifically minded people started doing more careful measurements on how gas volume changes with temperature.
Like what good science students do in school, they must have plotted points on graphs of volume against temperature. And they saw something surprising.
They saw that when they extended the straight line through the points measured, the lines always meets the temperature axis at the same point!
That point falls on -273.15 degree Celsius, in modern units. This probably happened no matter what gas they used, and how much gas they used.
There must have been all kinds of speculations among scientists about why this happened. Eventually, scientists understood that this was the lowest temperature possible. It is not possible to go below this temperature.
And they also invented another scale - the Kelvin scale. 0 Kelvin is -273.15 degree Celsius. Conversely, 273.15 Kelvin is 0 degree Celsius.
Going back to expanding and contracting gases, scientists found that if temperature of a volume of gas is doubled, then the volume of the gas also doubled - as long as we are careful to keep the pressure the same.
If instead we keep the volume fixed and double the temperature, then the pressure would double.
Or if we fix the temperature but increase the pressure on a gas, the volume would become half the starting volume.
With this understanding, they could make a simple formula relating pressure, volume and temperature. This the formula a student of physics has to learn in school - called the "ideal gas law".
But why add the word "ideal"? Does this mean it is not real?
Well, it is kind of real, but not very real. If we use this law to calculate pressures, volumes or temperatures of real gases, it may be fairly accurate for the common gases under normal temperatures and pressures.
But if the gas gets too cold, for example, or pressure too high, the gas law formula would be less and less accurate. One reason, for example, could be when the gas is so cold or molecules get so close - that it wants to condense into a liquid. Then it does not behave like a gas any more !
Avogadro (1856) was an Italian scientist. He is famous for his theory on molecules - now known as Avogadro's law. The law states that equal volumes of gases - with the same - temperature and pressure - contain the same numbers of molecules.
In physics, there are a number of "constants" that we have to learn. These are numbers that use for calculations. Examples are speed of light and acceleration due to gravity (like when we drop a stone to the ground).
There is one number, or constant, that has always intrigued me. This is the Avogadro constant: 6.02 x 1023. This is the number 602 followed by 21 zeros. It lets us calculate the number of molecules in a substance.
For example, the number of molecules in 32 grams of an oxygen gas is equal to the Avogadro constant. 32 is what is called the relative molecular mass of an oxygen molecule, and can be obtained by referring to the periodic table.
What I find intriguing is how this number 6.02 x 1023 is measured - over 100 years ago ! After googling on the history of this topic for a bit, I found that it was actually determined indirectly from the electric charge on a single electron - which was in turn measured some years later by another scientist called Millikan - in a method called the "oil drop experiment".
The above is likely more technical than I had wanted to write for a simple blog. But I think I should include this detail as some students of physics may find it interesting. This is bit of detail that is not normally mentioned in textbooks or taught in in school.
For students who are curious about how a weird number like the Avogadro number comes about, it would be satisfying to know about this connection with Millikan's oil drop experiment - which they may also have to learn in A level physics.
And to add a bit of gossip (physics after all is a human activity), Millikan's oil drop experiment was really done by his student Harvey Fletcher. Millikan "persuaded" Fletcher to give him all the credit, in return for getting the PhD degree. So Fletcher got his PhD, and Millikan got tne Nobel prize. Fletcher kept the agreement a secret until his death.
Anyway, coming to our gas - a volume of gas would likely have a very huge number of molecules inside. The kinetic theory of gases is a theory that tries to use few simple ideas to explain how these tiny molecules affect the pressure, volume and temperature of the gas.
By making a few simple assumptions, it turns out to be possible to calculate things like pressure, temperature and volume from the mass and velocities of the molecules. But what are assumptions?
An assumption is basically a guess. For example, we guess the following about say a bottle of nitrogen gas:
1. The gas is made up of tiny particles. (Today, we know these are molecules.)
2. The volume of a particles is very small compared to the container.
3. When two particles collide, the collision time is very small compared to the time to the next collision.
4. The particles do not attract or repel each other from a distance.
5. The particles are in random motion.
One or two hundred years ago, scientists probably thought of these ideas for fun. Today, it has become very important in things like car engines, refrigerators and other devices that makes use of gas flow.
So how does the movement of molecules give pressure, and how is the movement related to temperature?
The idea about the cause of gas pressure is to think about the tiny molecules hitting the wall of the container. Each molecule is tiny, but when you have Avogadro's constant kind of numbers - about 6 followed by 23 zeros, or 1 trillion trillion molecules - hitting the wall, the pressure is not small any more.
With simple understanding of momentum and force, it turns out to be possible with some maths to find a formula that relates temperature to kinetic energies of the molecules.
This also turns out to be one of the key steps to understanding what really is heat and temperature. In simple words, temperature is directly related to the average kinetic energy of the molecules. That means if something is hotter, it is because the molecules are moving or vibrating faster.
From the above understanding, we see a direct connection between two apparently very different types of energies: heat energy and kinetic energy of the molecules.
You can learn these concepts and more at Dr Hock's maths and physics tuition.