Thermal Expansion

Coefficient of volume (CUBICAL) expansion:
  
 It is defined as the ratio of increase in volume of a solid per degree rise of temperature to its initial volume.
If  v₁ and v₂ be the areas of a isotropic solid at t₁⁰C and t₂⁰C respectively then the coefficient of superficial expansion \(\gamma\) is given by
\(\gamma = \frac{{{v_2} - {v_1}}}{{{v_1}\left( {{t_2} - {t_1}} \right)}}\)……..(1)
(or) \({v_2} = {v_1}\{ 1 + \gamma \left( {{t_2} - {t_1}} \right)\} \)
\({v_2} - {v_1} = {v_1}\gamma \left( {{t_2} - {t_1}} \right)\)
Let \({v_2} - {v_1} = \Delta v,{v_1} = v,\left( {{v_2} - {v_1}} \right) = \Delta \)
then \(\Delta V = V\gamma \Delta t\)
% change in volume \(\frac{{\Delta v}}{v} \times 00 = \gamma \Delta t \times 100\)
 \(\frac{{\Delta v}}{v} \times 00 = 3\alpha \Delta t \times 100\)           
 “ \(\gamma\)” has units °C (C.G.S) and K^-1 (S.I.).
Values of coefficient of volume expansion for some solids and liquids