How does, thermodynamically, heat transmit through hard surfaces?

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Say you bring in a sealed box full of ice into a warm room. Knowing, thermodynamically, that higher temperature means higher energy of air particles that transfer heat by bumping into one another (don’t kill me for this oversimplification!), how does heat transfer across the hard box sides into the inner space and melt the ice?

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Particles in solids also “bump into each other”. They are more tightly packed and interact with all of their neighbors constantly. Imagine a net consisting of small balls connected with springs. If you move one ball, the springs will transfer the movement to other balls. That’s how solids transfer energy within themselves.

Air particles bump into particles on the outer layer of the box, they bump into slightly deeper particles, they bump into even deeper particles and so on, the particles on the inner side of the box bump into the particles of ice / colder air inside the box.

The innermost particles start losing energy after collision with ice (and outermost particles of ice gain this energy). They, in turn, receive some of the energy back from collisions with other particles of the box and so on.

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