Chemical Engineering Basics - Engineering

Q1:

The bulk modulus of a material with Poisson's ratio of 0.5 is equal to

A 3 x Young's modulus

B Young's modulus

C infinity

D zero

ANS:C - infinity

The relationship between Young's modulus (E), Poisson's ratio (ν), and bulk modulus �K) for an isotropic material is given by the following equations: K=3(1−2ν)E​ Given that Poisson's ratio (ν) is 0.5, we can substitute this value into the equation: K=3(1−2(0.5))E​ K=3(1−1)E​ K=3(0)E​ Since the denominator is 0, we have a division by zero error. This indicates that the bulk modulus (K) is undefined for a material with Poisson's ratio of 0.5. In practical terms, a material with a Poisson's ratio of exactly 0.5 is a theoretical construct and doesn't exist in real materials. Poisson's ratio for common materials typically ranges between 0 and 0.5. Therefore, the bulk modulus would not be defined for such a material.