Connect to the circuit neutral wire which should also be white.
The white wire would go to the neutral bar. Just be sure of the shunt trip voltage required for the breaker and land the white wire on the appropriate neutral bar in the correct panel.
If you are connecting 120 volts, you connect the black wire to the breaker, white wire to the neutral bar, and ground wire to the ground bar. If you are connecting 240 volts connect the black & white wires to the breaker, & ground wire to the ground bar.
You would need to take the "input" wire for the shunt trip breaker to an electrical switch (not alarm initiating switch, which are DC voltage rated) within the Automan unit and connect to the "Common" connection and the "return", the wire to the actual shunt circuit of the breaker, from the "Normally Open" connection of the switch. When the unit activates, the switch will be placed into "Closed" position, therefore completing the circuit and activating the shunt coil.
There is 220 volts between the two poles. If you are running 2 wires (black and white) + ground then you hook black to one pole and white to the other. Put red or black electric tape on each end of the white wire and wrap around wire for 3 inches or so next to the connection so the next person will be able to see that the wire is hot and not a neutral.
If you connect the ground wire to the hot wire it will trip the breaker. If you get the white and black wires reversed it will still work but does not meet code.
In the heater you will have two wires. You should then have 2 supply wires from the panel, and 2 wires from the thermostat. The neutral (white) supply wire should go to one of the wires on the heater. The hot (black) supply wire should connect to one wire from the thermostat. The other wire from the thermostat will connect to the other wire from the heater.
Assuming the wires are the correct gauge for application and breaker you use black and white wires as hot. Put red electrical tape on each end of white wire and connect red and black to the breaker output and bare wire to ground lug in panel. At receptacle connect black and red to hot contacts and bare wire to ground lug.
Ground wire connects to the ground bar, white wire connects to the neutral bar, and black wire connects to the breaker. Be sure and turn off main breaker before installing the wire or the breaker.
If you are referring to house wiring then the answer is no. A breaker protects the wire size that is connected to the breaker. In home wiring most homes are wired with a #14 wire which is rated at 15 amps. That is why the wire is protected by a 15 amp breaker. The correct wire size to connect to a 40 amp breaker is a #8. This size wire is too large to connect to receptacles an light fixture terminals.
There are per-engineered shunt trip solutions such as the Littelfuse LPSM that have a transformer that isolates the line voltage from the control voltage. You simply wire the N.O. contact on the float in the shunt trip isolated contacts.
the easiest way to tell, is the shunt trip breaker will actually take up 4 spaces in your panel. the 4th space will have a neutral wire coming out of it, along with a lug for power INPUT. when voltage is applied to the shunt trip, it will cause the other 3 poles to open by tripping the breaker.
There should be two outputs on the 30 A breaker. You will need 10 AWG wire with 3-conductors and ground. Typically the wire colors will be Black, Red, White and (Green or bare). Connect black to one output of breaker and red to other output. Connect white to the white buss bar in main panel and green/bare to ground buss bar. At heater end connect the red and black to the 240 V leads, white to white and green/bare to the heater case.