How is heat transferred away from the surface of the moon?

the heat is transferred away from the Moon’s surface through radiation.

In general, the heat can be transferred through conduction, convection or radiation.

Conduction is the transfer of heat by microscopic collisions of particles and movement of electrons within a body (solid, liquid or gas) or two bodies in contact, from parts at high temperature to parts at a lower temperature. Thermal energy appears as an oscillation of molecules of the material, which increases with the increase in temperature. During this oscillation, molecules hit each other, exchanging momentum, and therefore energy.

Convection happens when a fluid (liquid or gas) touches a solid at a higher temperature: increasing the temperature, the fluid expands and lowers its density, and, due to Archimedes’ principle, climbs up being less dense than the rest of the fluid, generating convection, in which the hot fluid climbs up and the cold fluid climbs down.

Radiation does not need direct contact between two exchangers and does not need a media to propagate. This is due to the fact that the heat transfer is made through electromagnetic waves. It is a phenomenon that happens in every material (solid, liquid or gas) and can happen in the vacuum. Radiation consists of the emission (or absorption) of electromagnetic waves (photons) generated by atoms and molecules making a transition from a high energy state to a lower energy state. 

Since the Moon does not have an atmosphere, its second exchanger is the vacuum and the only heat transfer possible is radiation.

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