Temperature – weirder than you think

Temperature is a pretty weird thing if you think about it. How do you best define temperature? Let me go ahead and give you my favorite definition:

Temperature is the thing that two objects have in common when they have been in contact for a long time.

Yes, that is a good definition. Maybe now you can see why temperature is weird. Doesn’t it have something to do with energy? Well, something – yes. Let me take an example. Suppose pour some hot coffee into a paper cup (I use paper because styrofoam(TM) is trademarked). Further suppose that this is super hot coffee from McDonald’s. Can you touch the paper and not be hurt? Yes. Can you touch the coffee and not be hurt? NO! However, they have the same temperature.

Why do the coffee and the cup have different effects even though they have the same temperature. There are two reasons. First, they have different amounts of ‘thermal energy’. I think the term thermal energy is a little vague, but it is useful. I will define thermal energy as the kind of energy that something has more of when it gets hotter. You may want to think of it as the kinetic energy of the atoms the material is made of. Hot coffee atoms (coffee should be on the periodic table) are moving faster than cold coffee atoms. So, when something is hotter than it was, it increases in some type of energy.

The other reason that the coffee and paper cup have different effects is what could be call specific heat. If you want, you can think of these two reason as really just “how much energy it has”. The coffee has more energy because there is more coffee than paper and coffee can also hold more energy per piece of coffee.

The coffee and the paper are interesting to consider since they have the same temperature but don’t act the same. Here is another great example. Suppose you are in a room with a rug on top of a ceramic floor. If they have been undisturbed, they will have the same temperature. Place your hand on the rug and then on the ceramic floor. Which one feels warmer? The rug will probably feel warmer. So, people are not very good at judging temperatures. Another good example is to comparing being in a room with 70 degree F air to being in 70 degree F water (very cold).

Ok, temperature is weird. But then what is it? How about I answer a different question? Suppose I put a cold piece of metal in room temperature glass of water. What will happen? If you say “the water will get colder and the metal will get warmer until they are at the same temperature” – then you are correct.

When that happens, the water decreases in thermal energy (where I have not really defined thermal energy) and the metal increases in thermal energy. In this case, I made it so that the two materials (water and metal) had the same, but opposite change in temperature. I just did that to make it easier to see, but clearly that does not always happen (depends on the mass of the two objects). What if the following happened?

Here, a cold metal is put into water. The result is that the water gets hotter and the metal gets colder (but energy is conserved). This would be an odd event. However, it is not really against the conservation of energy (which has been shown to be very reliable). So, why does the first case happen and the second one is never seen? It turns out that the probability of the second case is extremely small. So, temperature is the state that the two systems together have the most probable outcome. In fact, this has a lot to do with entropy. I am not going to go into that, but Built on Facts has a nice little post about entropy to get you started.

1. #1 humorix
March 7, 2009

It is to say that the Earth will turn more quickly if it is hot? (what could confuse the magnetic field?)

2. #2 dr. dave
March 7, 2009

Do you have a reference for that casual temperature definition in the box? I’ve never heard it put quite that way, and I think it would be a handy corollary to give my students after telling them the formal “Zeroth Law”

If not, I shall reference YOU.

3. #3 Tom
March 7, 2009

Depending on the details of the cup, the outside of the cup is probably at a lower temperature than the coffee, since the cup is contact with the air. A casserole dish in the oven, in thermal equilibrium, would be a somewhat better example. You don’t burn yourself just by sticking your hand in the oven, you burn it when you grab the dish.

4. #4 Uncle Al
March 7, 2009

Temperature is the thing that two objects have in common when they have been in contact for a long time.

Take a thin single crystal of platinum oriented [111] and polish that front and [-1-1-1] rear optically flat in hard vacuum. Vacuum metallize one face with a thick layer of elemental potassium. Store the sandwich suspended (free fall) in hard vacuum in the dark.

The platinum and potassium have intimately contacted front ends. Will the platinum and potassium layers ever equilibrate to the same temperature at any ambient temperature above absolute zero after an arbitrarily long aging period in hard vacuum? Thermally short the backsides with a bridging copper wire to make it much worse (kinetics). Vacuum work functions are Pt = 5.93 eV, K = 2.29 eV

5. #5 Rhett
March 7, 2009

@dr. dave,

I think a great place to look at this temperature stuff is in the Matter and Interactions textbook by Chabay and Sherwood. This is also discussed in the article by D. V. Schroeder “A different approach to introducing statistical mechanics” American Journal of Physics vol. 65 Jan 1997.