The temperature of a wire is doubled. The Young’s modulus of elasticity

The correct option is: will decrease.

Detailed Explanation:

Young's modulus of elasticity, denoted by
$Y$
is a measure of a material's stiffness. It is defined as the ratio of tensile stress, denoted by
$\sigma$
to tensile strain, denoted by
$\epsilon$
in the elastic deformation region:

$Y=\frac{\sigma }{\epsilon }$

At the atomic scale, the atoms in the wire are held in a lattice structure by interatomic forces. These forces can be modeled as tiny springs with an effective force constant, denoted by
$k$

When the temperature of the wire is increased, the thermal energy of the atoms increases, causing them to vibrate more intensely. Due to the asymmetry of the interatomic potential energy curve, the average distance between the atoms increases, leading to thermal expansion.

As the interatomic separation increases, the strength of the bonds holding the atoms together weakens, which reduces the effective force constant of the bonds. Since the Young's modulus is directly proportional to this force constant, the overall stiffness of the wire is reduced. Thus, as the temperature is doubled, the Young's modulus of elasticity will decrease.