Is this feasible? What parts do I need?

hello there, first post on here, registered see if idea can happen , if i'm doing right stuff far.

i eventually:
-make design small possible using custom printed board
-input 120v wall outlet
-have display on board
-potentiometer or button input selecting heating temp

anyway, trying use pid program on arduino board precisely control , monitor temperature of coil heater. familiar pid tuning. coil is  250w-120v , has thermocouple(temp sensor) built end. assume need ssr control , supply power coil.
looking at: 5a ssr
                                   input voltage 3-32vdc output voltage    380vac switch method    zero-cross turn on

i need putting together. how connect thermocouple arduino? how output arduino heat coil?

to connect thermocouple  arduino should use signal conditioning ic max31855.  see tutorial:

https://learn.adafruit.com/thermocouple/

to turn heater on, set output pin controlling ssr high.  turn off, set low.

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