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

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