[Physics] How hot does the tip of a pencil get while writing

everyday-lifefrictionheat

When writing with a pencil, there seems to be quite a lot of friction – which seems like it would induce heat.

How hot would the tip of a #2 pencil get writing on normal copy paper?

Best Answer

Graphite (pencil "lead") is an allotrope of carbon that occurs in layers of carbons arranged into hexagons, tessellating the plane. Each carbon is $sp^2$ bonded and each layer is one atom thick. The bonds holding the carbons in one plane together are incredibly strong, uniform covalent bonds of strength ~1.33, and the carbons are in a very stable hexagonal arrangement. These bonds are incredibly difficult to break, hence graphite's extraordinarily high melting point (several thousand kelvins).

By contrast, there are only weak dispersion forces holding different planes together, which are easily broken. When you write, you are breaking these bonds to leave graphite layers on the paper.

Imagine a deck of cards. Even if you're the fastest dealer in the world, the deck never heats up. Why? Because however much friction is felt at the interface between the top card and the one under it, it is only felt for a moment and then new, cool cards feel it.