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

With rise in temperature, the Young's modulus of elasticity generally decreases for most materials.

Concept Used:

Young's modulus (E) is defined as the ratio of stress to strain in the elastic region of a material. It is a measure of the stiffness of a material. The temperature dependence of Young's modulus is related to the interatomic bonding forces and thermal expansion of the material.

Step-by-Step Explanation:

Step 1: Understand the relationship between interatomic forces and Young's modulus.

Young's modulus is given by \( E = \frac{\text{Stress}}{\text{Strain}} \). At the atomic level, it depends on the curvature of the potential energy curve between atoms: \( E \propto \frac{d^2U}{dr^2} \), where U is the interatomic potential and r is the interatomic distance.

Step 2: Consider the effect of temperature on interatomic spacing.

As temperature increases, materials expand due to increased atomic vibrations. This increases the average interatomic distance (r). For most bonding potentials, the second derivative \( \frac{d^2U}{dr^2} \) decreases as r increases beyond the equilibrium position.

Step 3: Analyze the effect on bond stiffness.

The force constant (k) of the atomic bond, which determines Young's modulus, decreases with increasing interatomic separation. Since thermal expansion causes increased interatomic spacing, the bond becomes less stiff, resulting in a decrease in Young's modulus.

Step 4: Consider exceptions and general behavior.

While most materials show a decrease in Young's modulus with increasing temperature, some materials like invar (a nickel-iron alloy) show minimal change due to their near-zero thermal expansion coefficient.

Therefore, with rise in temperature, the Young's modulus of elasticity decreases for most materials.