Interpretation:
The change in volume of polyethene after applying a uniaxial stress has to be calculated.
Concept Introduction:
Poison ratio can be calculated as follows,
poison ratio, σ =transverse strainuniaxial strain
Strain can be calculated as follows,
strain=change in dimensionoriginal dimension
Contraction in both transverse directions occurs during transverse strain.
Answer to Problem 15D.3AE
The change in volume is calculated as 9.3×10-4 cm3.
Explanation of Solution
Consider (ΔLL)z is the uniaxial strain, and (ΔLL)x, (ΔLL)y are the transverse strain.
(ΔLL)x=(ΔLL)y.
When the stress is applied the length in the transverse direction decreases, but length in axial direction increases.
Given information is shown below,
(ΔLL)z=0.01σ=0.45Initial volume of the cube,V=1 cm3Initial side length of the cube ,Lx=Ly=Lz=1 cm
Therefore transverse strain can be calculated as follows,
transverse strain=σ×uniaxial strain=0.45×0.01=4.5×10-3
So, (ΔLL)x=
Change in length in z direction can be calculated as follows,
Therefore the new length in the axial direction (
Change in length in x and y direction can be calculated as follows,
Therefore the new lengths in the transverse directions (
The new volume of the solid can be calculated as follows,
Therefore the change in volume can be calculated as follows,
The change in volume is calculated as
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Chapter 15 Solutions
Student Solutions Manual to accompany Atkins' Physical Chemistry 11th edition
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