### Question

If temperature is 'The average kinetic energy of particles' (i.e. if you measure the temperature of a cup of water it is the average of all the water molecules in the cup), then how does one determine the temperature of a vacuum? (Division by zero error)

One doesn't determine the temperature of a vacuum. Just as 'nothingness' has no color, taste, smell, etc. it also has no temperature. That is because, as you point out in your question, there are no particles whose kinetic energy can be measured or averaged.

Only objects within a vacuum can have a temperature, and that temperature will depend on the balance of incoming and outgoing radiation. Electromagnetic radiation can travel through a vacuum, so objects in space of any temperature above the near absolute zero (0 Kelvin = about -273 deg C.) temperature of cosmic background radiation (which is about 3 Kelvin) will radiate energy into space. Without another source of energy replacing that loss (a nearby Sun, for example) the object's temperature will decrease. That is why you read about 'the coldness of outer space'.
Answered by: Paul Walorski, B.A. Physics, Part-time Physics Instructor

### Science Quote

'Strange is our situation here upon the earth. Each of us comes for a short visit, not knowing why, yet sometimes seeming to divine a purpose.'

Albert Einstein
(1879-1955)