A uniform, isotropic solid block is heated through a small temperature interval.
a. (i) Define the coefficients of linear expansion (α), superficial expansion (β) and cubical expansion (γ) of a solid.
b. (ii) Qualitatively explain how an increase in length in each dimension leads to corresponding increases in area and volume. Hence justify, without detailed calculation, why β is approximately twice α and γ is approximately thrice α for small temperature rises.
c. (iii) State any two practical situations in engineering where neglecting the difference between the exact and approximate relations among α,β and γ could lead to significant error, briefly giving the reason in each case.