Increase in temperature when a stretched wire suddenly snaps

Question

When a wire is stretched under a force F so as to obtain an increase in length Δl the work done by the external force on the wire is

(FΔl)

Now the work done by the wire against the force is

1/2(FΔl)

This work is stored as the potential energy
And heat produced is

1/2(FΔl)

So when the wire snaps the energy stored in the wire will be converted into heat so as to increase the temperature of the wire ( or I'm wrong?)
Any help will be greatly appreciated.

Gert · Answer

If your wire is perfectly elastic, then heat doesn't play a part in this.
But if it isn't perfectly elastic a phenomenon called hysteresis comes into play:

The energy needed for 'loading' (i.e. stretching) the wire is the area under the blue curve. The energy needed for 'unloading' (i.e. recovery) the wire is the area under the red curve.
Obviously the two aren't equal and the difference is heat energy.
In the perfectly elastic case, say your wire breaks at $Δl$ then the energy to break the wire will be $W=int_0^{Δl}F(l)rm{d}l$ (because $F$ will depend on $l$), without any heat loss due to hysteresis.

Increase in temperature when a stretched wire suddenly snaps

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