Question

With rise in temperature, the Young's modulus of elasticity

• A. changes erratically
• B. remains unchanged
• C. increases
• D. decreases

Answer 1

The Correct Option is D

For the majority of materials, Young's modulus of elasticity generally declines as temperature rises.

Concept Used:

Young's modulus (E) quantifies a material's stiffness, defined as the ratio of stress to strain within its elastic limits. Its temperature dependency is linked to interatomic bonding forces and thermal expansion.

Step-by-Step Explanation:

Step 1: Relate interatomic forces to Young's modulus.

Young's modulus is expressed as \( E = \frac{\text{Stress}}{\text{Strain}} \). At an atomic level, it is proportional to the curvature of the interatomic potential energy curve: \( E \propto \frac{d^2U}{dr^2} \), where U is the interatomic potential and r is the interatomic distance.

Step 2: Examine temperature's effect on interatomic spacing.

Increased temperature causes greater atomic vibrations, leading to thermal expansion and an increase in the average interatomic distance (r). For most bonding potentials, the second derivative \( \frac{d^2U}{dr^2} \) decreases as r increases beyond equilibrium.

Step 3: Assess the impact on bond stiffness.

The force constant (k) of atomic bonds, which dictates Young's modulus, diminishes with greater interatomic separation. As thermal expansion increases this separation, the bonds become less stiff, consequently reducing Young's modulus.

Step 4: Discuss exceptions and general trends.

While most materials exhibit a decrease in Young's modulus with rising temperature, certain materials like invar (a nickel-iron alloy) demonstrate minimal change due to their exceptionally low thermal expansion coefficient.

Consequently, for most materials, Young's modulus of elasticity decreases as temperature increases.