If temperature is proportional to average kinetic energy, then is the air around me actually at a higher temperature than, say, my table?

Question

I know that thermometers work by conduction, meaning that the particles in the alcohol inside the thermometer will always get to the same average speed of the particles of the surrounding substance that you're measuring (as long as you leave the thermometer in the substance for long enough). So it seems to me that if I left a thermometer long enough in the air around me, then the thermometer should register a higher temperature in degrees Celsius for the air than if I left a thermometer for long enough in a solid like my table (assuming that the solid had a snug hole for the thermometer to occupy). I think this should be true because the particles in the air are moving faster on average than those in the table, and so should cause the alcohol particles in the thermometer to also reach a faster speed than the table would cause them to, meaning that the alcohol should expand more for the air and so register a higher temperature on the scale. I know the particles in the air are moving faster on average than those in the table, because the air is a gas, and particle theory states that particles in gases whizz around faster on average than particles in solids that can only vibrate around fixed positions. The mark scheme of an exam paper I was marking also said that when you melted a liquid to form a gas, the gas particles had more kinetic energy than the liquid particles had had.

But if this is true, then how did the air get to this higher temperature when the table didn't, even though they are both in the same environment? Is it because maybe the air had a lower specific heat capacity than the table, meaning that the same number of joules of energy (say 20j) would get the air to a higher temperature than it would get the table to, because a higher proportion of that energy would be going into the kinetic energy store of the air (say 15j of it) than it would the kinetic energy store of the table (say, only 7j of it) (because more of the energy would be going into the potential energy store (say 13j) in the case of the table)???

I'm getting so confused trying to reconcile all the different truths about KE, temperature, specific heat capacity and melting and boiling points as soon as I am trying to think about them at a deeper level, maybe because I don't have enough relevant information about them except for the simple facts and equations: please help! Thanks so much.

Answer 1

You say you think particles in the air are "obviously" moving faster than those in the table. Why do you think this?

Imagine a huge structure made out of some balls connected by springs. Imagine giving this structure a shove: you would see a lot of motion, even if the overall structure was so big compared to the shove you gave it that it doesn't move across the ground. That motion is analogous to (if you're willing to have a simplified model) the motion of atoms within the molecules of your table, and it's the motion of each atom (ball) which you should be comparing to the motion of air molecules, not the structure as a whole.

Just as if you were to throw a ball at this imagined structure, when you calculate the result of any collision between an air atom and a table atom, you only need to care about the instantaneous momentum of each atom, not the rest of the world they're in (again, I'm simplifying: if the atoms hit hard enough either the table atom breaks away or the table atom and air atom stick together, but that's more about why water evaporates than why tables can be the same temperature as the air around them).

Indeed, it is the extra degree of freedom of motion given by vibrations (and all the other things I'm ignoring) which are the reason why specific heat capacities vary by material, as the energy is spread between each degree of freedom.

Answer 2

I think this should be true because the particles in the air are obviously moving faster than those in the table

How can you determine this? The particles in the air can go farther because they are not bound together. But directly comparing the speed is difficult.

In fact, the particles making up the table are moving quite quickly. But the bonds restrict their motion to a small region. But when the particles do interact (say because a gas molecule bumps into it), they can exchange momentum.