6. Measurement of Heat and Thermal Expansion

Relationship to Linear Thermal Expansion Coefficient

For isotropic material, and for small expansions, the linear thermal expansion coefficient is one third the volumetric coefficient. To derive the relationship, let’s take a cube of steel that has sides of length L. The original volume will be V = L3,and the new volume, after a temperature increase, will be:


The approximation holds for a sufficiently small ΔLΔL compared to L. Since:

ΔV / V=3ΔL / L

(and from the definitions of the thermal coefficients), we arrive at:


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