Can two different objects or system of molecules have different temperatures, but having same internal kinetic energy?

If I take an extreme case, where a body has only an internal potential energy with zero internal kinetic energy, does this body have a temperature? Another question related to it: if two objects A and B having different temperature: A: having only internal potential energy and B having only internal kinetic energy, can heat flow from A to B ?(temperature of A > B)

• If A has only internal potential energy, its temperature is 0°K. It can't be hotter than B. – Peter Shor Jun 28 '16 at 15:30

Yes. According to the accepted theory of gases, a diatomic molecule (like N2) has both translational kinetic and rotational kinetic energy, five partitions (two rotation axes, and three directions of travel in space), which each can hold kT/2 energy, on average, for a total thermal average energy of 5kT/2. A neon atom, on the other hand, cannot hold rotational energy (it is too cold, at any ordinary temperature, to hold one quantum unit of angular momentum along any of the three directions), so holds a total thermal energy of 3kT/2.

So, air (containing both neon and nitrogen) fits the description.

Different amounts of energy at the same temperature means different heat capacities, there are many examples (and this is only one).

• Great. Then if both have different kinetic energies why there's no transfer of heat between them? (I know both are at same temperature) – Tonylb1 Feb 11 '16 at 20:36
• It's not possible for a spinning diatomic molecule (N2) to transfer – Whit3rd Feb 12 '16 at 9:56
• Sorry, but this answer does not seem to answer either of the questions asked. – porphyrin Jun 28 '16 at 14:22
• A transfer of heat DOES happen from time to time, but the complex (diatomic) molecule has multiple heat-containing modes (including rotation of the molecule) and the monatomic gas can only gain/lose momentum in three directions. Statistically, the extra modes of the N2 molecule mean it has more heat energy per molecule, on average, than the Ne atom. Actually, Ar (argon) is a more likely air constituent. – Whit3rd Jul 4 '16 at 22:56

If a body (substance) has zero kinetic energy then we should suppose that it is a perfect crystal at absolute zero and all motion is in the vibrational ground state if it is a molecule. If an atomic solid then only zero point motion in the lattice. So yes it has a temperature. The potential energy is that within and between the molecules or atoms.
In your second question if the temperature is different in two isolated bodies but in contact with one another then energy will flow from one to the other until equilibrium is reached. Energy is always convertible from one form to the another.

• Energy is always convertible from one form to another???? Consider a chemical explosive at close to 0°K. It has an enormous amount of internal potential energy. It has very little internal kinetic energy. Is its chemical potential going to spontaneously turn into heat? How long do you have to wait for this to happen? I think this is essentially the OP's question, but I'm not sure. – Peter Shor Jun 28 '16 at 15:29
• Yes, energy is always interconvertible, we see it happen all the time. Molecules convert potential energy into kinetic energy and vice versa every time they vibrate in their normal modes. Your explosive molecule does have zero point energy, kinetic and potential at 0 k and bond energy. It always has the potential to explode but only if you give it enough energy to reach the activation energy will it do so rapidly. We exist at room temperature and are exothermic wrt burning in oxygen, luckily activation barriers are large. Thermodynamics says nothing about the rate of reaction. – porphyrin Jul 24 '16 at 20:18