how do you replace a t r v s on a 10 mm copper pipe.?

Answer 1

With difficulty. Some Trv's come with spare fittings to be able to fit onto different sized radiator valves. Ask around, best try a plumbing shop, i.e plumbase/plumbcentre. 10mm is very unusual pipe work, not often seen.
Alternative is to replace pipework either just on sections required, or perhaps all if you are really keen, and increase pipework up to fit normal 15mm copper pipe via reducer fittings, just vice versa. Good luck

Answer 2

Simply buy a new trv from a good plumbers merchant,along with a 15x10mm insert,bush or reducing coupling.This way,you can buy a standard 15 mm trv available antwhere.You may also need a short section of 15mm tube to make up any discrepancy in overall length.

Answer 3

Is this a radiator valve?

Buy a new one, isolate the water supply, remove the old one with an adjustable spanner and replace.

Answer 4

Gently