# Q & A: temperature questions

Q:
1. Absolute zero is a minimum temperature. Is there a maximum temperature? Explain 2. What is the temperature of a vacuum?Explain 3. A metal ball can pass through a metal ring. When the ball is heated, however,it gets stuck in the ring. What would happen if the ring, rather than the ball, were heated? 4. Explain why lakes freezes first at the surface.
- prisco (age 39)
philippines
A:
1. At absolute zero, things have fallen into the lowest energy state that they have.  Infinite temperature would mean having an equal chance to be in any of the possible states. However, the states just keep going on up to higher and higher energy. For example, you can have states with any number of photons. As the chance of being in any state gets close to equal, the average energy blows up toward infinity. So with some finite amount of energy around, the temperature stays finite. With more energy, it could always get larger, so there's no upper limit.

2. A vacuum can have any temperature. The temperature determines how much random thermal radiation, mostly electromagnetic waves, is present. The vacuum of distant space happens to have a temperature just under 3K, very cold but not as cold as one can reach in an ordinary lab. At temperatures over about a billion K not only electromagnetic waves but even electrons and positrons start to show up. I guess at that point, you might want to stop calling a vacuum by that name.

3. Assuming the ring were made of similar material, it would also expand, making it easier for the ball to pass through.

4. Usually the heat is flowing out to the cold air from the surface. The bottom is usually warmer than the air, if it's been sitting under liquid water. It helps that when water gets below 4°C, it actually expands a little, getting less dense. That means that the coldest water can just float on top, where it can cool down even more.

Mike W.

(published on 10/22/2007)

## Follow-Up #1: thermal equilibrium

Q:
Can one object be hotter than another if they are at the same temperature? Explain.
- Anonymous
A:
No, what we mean by 'hotter' (in this context) is 'having higher temperature', so by definition that's impossible. One object might feel hotter, but that's only because it might conduct heat better than the other.

This reminds me of another important principle. If two objects can freely exchange energy they will come to the same temperature. That's because entropy S is spontaneously maximized (for reasons that are still argued about). The answer to your other question says that the higher T means lower dS/dU. So having energy U flow from higher T to lower T raises S more for the cold object than it lowers S for the hot object.

Mike W.

(published on 10/22/2007)

## Follow-Up #2: 0°C

Q:
Water of 0 degree celsius is warmer or ice of the same temperature????????
- Vasishta (age 11)
A:
They're both at the same temperature, so neither one is warmer.

Mike W.

(published on 05/16/2013)

## Follow-Up #3: temperature in energy units

Q:
can we define temperature as a derived quantity in terms of length ,mass and time?
- ghulam sabir (age 22)
pakitan
A:
Certainly. Modern books on statistical physics often get rid of the old convention of measuring temperature in "Kelvin" and then multiplying by Boltzmann's constant to get the thermal energy scale. Instead they simply use energy units (for examples,  joules or ergs) for temperature. So in terms of length, mass and time, it's just mass*length2/time2.

Mike W.

(published on 03/04/2013)