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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

Show that the coefficient of volume expansion, β, is related to the coefficient of linear expansion, α, through the expression β = 3α.

To determine
The relation between the co-efficient of linear expansion ( α ) and co-efficient of volume expansion ( β ).

Explanation

Formula to calculate the volume of a solid at a temperature T0 is,

V0=A0L0

  • A0 is the cross sectional area.
  • L0 is the length of the solid.

When there is a change in temperature, A0 and L0 also change.

The change in temperature is,

ΔT=TT0

The area (A) at temperature T is,

A=A0(1+2αΔT)      (I)

The length (L) at temperature T is,

L=L0(1+αΔT)       (II)

Formula to calculate the volume of a solid at a temperature T is,

V=AL       (III)

Substitute Equations (I) and (II) in (III).

V=A0L0(1+2αΔT)(1+αΔT)

Substitute V0 for A0L0 in the above equation

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