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So on a macroscopic level, there is physical contact and the heat energy is being transferred from the higher temp. to lower temp. But what about in a microscopic level, what's going on?

As far as I know temperature can be defined as a measure of the average kinetic energy of the particles in a system. So I assume the particles with higher kinetic energy transfer it to the particles with lower kinetic energy? If this is true, how? Again as far as I know kinetic energy can be transferred through collisions. For example, we have a mug of hot coffee. Is it because the particles in the coffee collide to the boundary which is essentially colliding with the particles in the mug?

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    $\begingroup$ Yes. That is the essence. You have already answered your own question. Atoms and molecules bumping into each other causing momentum transfer and thus kinetic energy transfer. This is heat conduction. $\endgroup$
    – Steeven
    Jan 9, 2019 at 11:36
  • $\begingroup$ temperature can be defined as average kinetic energy per particle ONLY for an ideal gas, i.e, for particles that are free to move in 3D without interaction except for mechanical collisions. In solids/liquids/real gases, ie. real matter, this is no longer true. $\endgroup$
    – hyportnex
    Jan 9, 2019 at 13:33

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There are 2 modes of heat transfer in solid materials - atomic movements and electrons.

Like you said, we can have atoms vibrating and transferring their energy to each other. In crystalline materials this happens in a wavelike manner and is called a phonon.

In noncrystalline materials (i.e., polymers, amorphous materials, random alloys, etc.) the vibrations are less wavelike and more random. Wavelike vibrations carry energy better than non wavelike vibrations, which is why crystalline materials have higher thermal conductivity.

In metallic materials, the atoms can still transfer vibrational energy to each other, but the electrons actually make up the majority of heat conduction. Electrons gain kinetic energy and transfer energy to each other by colliding, similar to a gas.

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