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Show that ? ? 3?, by calculating the change in volume ?V

College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs ISBN: 9781938168000 42

Solution for problem 21PE Chapter 13

College Physics | 1st Edition

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College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs

College Physics | 1st Edition

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Problem 21PE

Problem 21PE

Show that β ≈ 3α, by calculating the change in volume ΔV of a cube with sides of length L. 13.3 The Ideal Gas Law

Step-by-Step Solution:
Step 1 of 3

Solution 21PE

1

The change in length is denoted by, the change in temperature is denoted byand the coefficient of linear expansion is denoted by, that varies slightly with temperature.

2

Assume Vo as the initial volume of the cube and Lo as its initial length so,

Vo=Lo3

V=Vo+

   = (Lo + 3

Substitutefor

V = (Lo + o)3

     = Lo3 (1 + 3

3

Sinceis small, binomial expansion is applied as,

V = Lo3 (1 + 3

      = (Lo3 + Lo3 3

      =Vo + 3Vo 

=3Vo 

SubstituteVo for 

Vo = 3Vo 

   

Hence, it is proved that

Step 2 of 3

Chapter 13, Problem 21PE is Solved
Step 3 of 3

Textbook: College Physics
Edition: 1
Author: Paul Peter Urone, Roger Hinrichs
ISBN: 9781938168000

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Show that ? ? 3?, by calculating the change in volume ?V