I have a 1" x 1"coil of 25awg coated copper wire about 50ft wrapped around a pvc tube, how much amperage would that coil be able to handle for exactly 1 second with free air around it?

 

You will have to experiment. And various other details matter.........like a repetition rate. Also it depends on the context. Is it just current for current's sake....or the M field.

It all depends on what you are doing.

 

I have a 1" x 1"coil of 25awg coated copper wire about 50ft wrapped around a pvc tube, how much amperage would that coil be able to handle for exactly 1 second with free air around it?

It depends what you mean by "handle". Sufficient heat will cause melting of the insulation. This won't immediately cause a short between turns but it will if the process is repeated. I suppose you could estimate the current required to vaporize the insulation and set it ablaze. Or to vaporize the copper itself.

There are magnet wire ampacity ratings available in tables. Have you looked at those? Lots and lots of data.
https://www.superioressex.com/uploa...t_Wire_-_Winding_Wire/EngData_book_linked.pdf