adeen says that you can increase the resistance of a copper wire by hammering the wire to make it narrower and longer. Arnell says that you can increase its resistance by heating the wire. Which one, if either, is correct, and why

Both of Arnell and Adeen are right.

Explanation:

For Adeen, hammering the wire makes it flat, effectively reducing the cross sectional area, and increasing the length of the wire. Recall that the resistivity of a metal conductor increases with length and decreases with cross sectional area. From this, we can see that the resistance of the wire will increase due to the hammering. This means Adeen is correct.

For Arnell, heating a metal causes the atoms along with their electrons to vibrate in a random manner. These random motions is not organised and can be in any direction. For electricity to flow smoothly, the electrons must travel in the same direction in an orderly fashion. The randomly vibrating atoms will continuously bump into the flowing electron, resisting the smooth motion of the electrons. This collisions results in an additional resistance, hence, the resistance is increased. This means Arnell is correct.