How Long Does It Take for a Comet to Evaporate in the Oort Cloud?

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Interesting question to think about.

We know that there are lots of comet bodies in the Oort cloud and we know that even in the near absolute zero temperatures evaporation does take place. Comets are usually covered in dust, which slows down this evaporation, but let's consider clear body.

How much time will it take to completely evaporate average comet body (of wafer ice) 10x5 km? Comet does not go around the sun - just sitting in the Oort cloud in the edge of the Solar System. Any good approximations?
 
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As I do not have the numbers at hand (nor do i know them by heart), I will only indicate how you could make such an estimate, if you need more help, please tell me so.

The comets in the Oort Cloud are probably fairly good black bodies. They do not have an atmosphere and will therefore have about their equilibrium temperature (they receive as much heat from the sun as they radiate away), so you can estimate their temperature. The temperature sets a distribution of energies of the particles inside the comet. The ones with an energy exceeding their evaporation energy will escape. This should give you a handle on the evaporation rate.

Whatever you calculate, the evaporation rate of a reasonably large comet should be extremely long!