Hi greetings

As two wires are connected in the series therefore the amount of current flowing through them will be same the difference in heat produced will be due to the difference in resistance we know that heat produced is I square R therefore the ratio of heat produced will be same as the ratio of resistance of the two wires.

One wire is 1 mm length and other is 2 mm therefore the second wire will have half the radius of first one. And we know that resistance is proportional to the ratio of length to area. Therefore the total heat produced will be double in the second wire compared to first wire.

Hope this helps all the best.