ATKINS' PHYSICAL CHEMISTRY
ATKINS' PHYSICAL CHEMISTRY
11th Edition
ISBN: 9780190053956
Author: ATKINS
Publisher: Oxford University Press
Question
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Chapter 15, Problem 15D.3AE
Interpretation Introduction

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,

  poisonratio, σ =transversestrainuniaxialstrain

Strain can be calculated as follows,

  strain=changeindimensionoriginaldimension

Contraction in both transverse directions occurs during transverse strain.

Expert Solution & Answer
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Answer to Problem 15D.3AE

The change in volume is calculated as 9.3×10-4cm3.

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=0.45Initialvolumeofthecube,V=1cm3Initialsidelengthofthecube,Lx=Ly=Lz=1cm

Therefore transverse strain can be calculated as follows,

  transversestrain=σ×uniaxialstrain=0.45×0.01=4.5×10-3

So, (ΔLL)x= (ΔLL)y=4.5×103.

Change in length in z direction can be calculated as follows,

  ΔLz=0.01×Lz=0.01×1cm=0.01cm

Therefore the new length in the axial direction (Lz') can be calculated as follows,

  ΔLz=Lz'LzLz'=ΔLz+Lz=0.01cm+1cm=1.01cm

Change in length in x and y direction can be calculated as follows,

  ΔLx=4.5×103×Lx=4.5×103×1cm=4.5×10-3cm

  ΔLy=4.5×103×Ly=4.5×103×1cm=4.5×10-3cm

Therefore the new lengths in the transverse directions (Lx'andLy') can be calculated as follows,

  ΔLx=LxLx'Lx'=LxΔLx=1cm(4.5×103)cm=0.9955cm

  ΔLy=LyLy'Ly'=LyΔLy=1cm(4.5×103)cm=0.9955cm

The new volume of the solid can be calculated as follows,

  V'=Lx'×Ly'×Lz'=0.9955cm×0.9955cm×1.01cm=1.00093cm3

Therefore the change in volume can be calculated as follows,

  changeinvolume,ΔV=V'V=1.00093cm3-1cm3=0.00093cm3=9.3×10-4cm3.

The change in volume is calculated as 9.3×10-4cm3.

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Chapter 15 Solutions

ATKINS' PHYSICAL CHEMISTRY

Ch. 15 - Prob. 15A.2AECh. 15 - Prob. 15A.2BECh. 15 - Prob. 15A.3AECh. 15 - Prob. 15A.3BECh. 15 - Prob. 15A.4AECh. 15 - Prob. 15A.4BECh. 15 - Prob. 15A.1PCh. 15 - Prob. 15A.2PCh. 15 - Prob. 15A.3PCh. 15 - Prob. 15A.4PCh. 15 - Prob. 15A.5PCh. 15 - Prob. 15A.6PCh. 15 - Prob. 15A.7PCh. 15 - Prob. 15A.8PCh. 15 - Prob. 15A.9PCh. 15 - Prob. 15B.1DQCh. 15 - Prob. 15B.2DQCh. 15 - Prob. 15B.3DQCh. 15 - Prob. 15B.1AECh. 15 - Prob. 15B.1BECh. 15 - Prob. 15B.2AECh. 15 - Prob. 15B.2BECh. 15 - Prob. 15B.3AECh. 15 - Prob. 15B.3BECh. 15 - Prob. 15B.4AECh. 15 - Prob. 15B.4BECh. 15 - Prob. 15B.5AECh. 15 - Prob. 15B.5BECh. 15 - Prob. 15B.6AECh. 15 - Prob. 15B.6BECh. 15 - Prob. 15B.7AECh. 15 - Prob. 15B.7BECh. 15 - Prob. 15B.11AECh. 15 - Prob. 15B.11BECh. 15 - Prob. 15B.12AECh. 15 - Prob. 15B.12BECh. 15 - Prob. 15B.1PCh. 15 - Prob. 15B.2PCh. 15 - Prob. 15B.3PCh. 15 - Prob. 15B.4PCh. 15 - Prob. 15B.6PCh. 15 - Prob. 15B.7PCh. 15 - Prob. 15C.1DQCh. 15 - Prob. 15C.2DQCh. 15 - Prob. 15C.1AECh. 15 - Prob. 15C.2AECh. 15 - Prob. 15C.2BECh. 15 - Prob. 15C.3AECh. 15 - Prob. 15C.3BECh. 15 - Prob. 15C.4AECh. 15 - Prob. 15C.4BECh. 15 - Prob. 15C.5AECh. 15 - Prob. 15C.5BECh. 15 - Prob. 15C.1PCh. 15 - Prob. 15C.2PCh. 15 - Prob. 15C.3PCh. 15 - Prob. 15C.4PCh. 15 - Prob. 15C.5PCh. 15 - Prob. 15C.7PCh. 15 - Prob. 15C.8PCh. 15 - Prob. 15C.9PCh. 15 - Prob. 15D.1DQCh. 15 - Prob. 15D.1AECh. 15 - Prob. 15D.1BECh. 15 - Prob. 15D.2AECh. 15 - Prob. 15D.2BECh. 15 - Prob. 15D.3AECh. 15 - Prob. 15D.3BECh. 15 - Prob. 15D.1PCh. 15 - Prob. 15D.2PCh. 15 - Prob. 15E.1DQCh. 15 - Prob. 15E.1AECh. 15 - Prob. 15E.1BECh. 15 - Prob. 15E.2AECh. 15 - Prob. 15E.2BECh. 15 - Prob. 15E.3AECh. 15 - Prob. 15E.3BECh. 15 - Prob. 15E.5PCh. 15 - Prob. 15F.1DQCh. 15 - Prob. 15F.1AECh. 15 - Prob. 15F.1BECh. 15 - Prob. 15F.2AECh. 15 - Prob. 15F.2BECh. 15 - Prob. 15F.3AECh. 15 - Prob. 15F.3BECh. 15 - Prob. 15F.4AECh. 15 - Prob. 15F.4BECh. 15 - Prob. 15F.5AECh. 15 - Prob. 15F.5BECh. 15 - Prob. 15G.1DQCh. 15 - Prob. 15G.2DQCh. 15 - Prob. 15G.1AECh. 15 - Prob. 15G.1BECh. 15 - Prob. 15.1IA
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