Atoms in motion - temperature and thermal energy
- Matter is made of atoms.
- Atoms can can form chemical bonds to other atoms, forming molecules, or solids.
- Atoms can move through space.
- The hotter an object is, the higher is its temperature, and the faster its atoms are moving.
- As atoms move faster and faster, a substance typically expands.
- As atoms move faster the bonds in a solid can break. We call this melting.
Evidence for moving atoms?
Atoms are, we think, moving all the time. You can't see the atoms directly (they are too small). But the motion of atoms causes larger objects to "jostle around".
We think this is the reason for Brownian motion.
Atomic motion and temperature
Here is a conceptual picture of molecules (in a gas) moving in a random and
disorganized manner.
With each collision, the
speed and direction of each atom changes.Is there anything that remains unchanging through all this change?
According to "kinetic theory" the thing that is constant is the average value of ($v^2$), which I'll write as $\langle v^2 \rangle$. And that this average is related to the temperature, $T$, of an object: $$k_BT=\frac12 m \langle v^2 \rangle.$$ [Temperature measured in Kelvin degrees (273 celsius degrees below temperature in Celsius) where -273 C = 0 K = "absolute zero".]
In other words, the hotter an object is, the faster its molecules are moving.
Einstein
made some calculations (1905) about how grains buffeted by random molecular
collisions would move which agreed well with experiment.Look up random walk or drunkard's walk. [children's activity]
- If a 'drunkard' wanders a city laid out on a square grid,
- at each intersection he randomly decides 1 of 4 possible directions to go next,
- he counts intersections as he goes, and counts $N$ of them.
- maybe passing through the same one many times--he doesn't know!
Einstein calculated that after he travels a total distance of $N$ intersections, he will on average be a distance $d=\sqrt{N}$ away from his starting point. [Though we have no idea of what direction away from his starting point he'll be.]
His calculation predicts that the distance a randomly buffeted particle moves away from where it start after a short time $\Delta t$, will be larger, the higher the temperature. Those calculations agree well with experiment.
[image: Wolfram math world]
Phases of matter
We know of 3 common phases of matter:
- Solid
- Liquid
- Gas
According to the atomic theory, these can be characterized as:
- Solid- The *average* position of molecule is not changing.
(So, how can the atoms in a solid be moving if that's the case??)
- Liquid- The average position of a molecule is not constant. Molecules are
free to move past each other.
A liquid in a container (e.g. in a glass) will not fill the container.
- Gas- molecules are moving, the average density of a gas is much lower than a liquid. A gas will completely fill a container.
See this simulation: tiny.cc/states. Pick "States" and Argon.
- Find a temperature at which the material looks "solid".
- Find a temperature at which the material looks "liquid".
- Find a temperature at which the material looks to be a "gas".
- Approximate temperature at which it's changing from solid->liquid.... or liquid->gas?
- Was there ever a temperature at which more than one "state" is present?
- Other observations?
Going from a liquid to a gas, atoms move somewhat faster, but also take up much more space. e.g. Water:
- 55.5 moles of liquid water takes up 1 liter of volume at 100 C.
- 55.5 moles of water vapor takes up 1300 liters at 100 C.
Temperature and expansion
Heating things up causes the atoms to bounce against each other harder and harder.
- Imagine you had a rubber bag full of atoms.
- As the atoms move faster they bounce harder against the rubber sides of the bag.
- What happens to volume of the bag?
Expanding when temperature increases
Image credits
Wikipedia - atmosphere, thermal motion
