What happens during the thermal expansion of a material when it is heated?

As shown in the figure,an equilateral triangle $ABC$ is formed by joining three rods of equal lengths $l$. $D$ is the midpoint of $AB$. The coefficient of linear expansion of the material of rod $AB$ is $\alpha_1$ and that of rods $AC$ and $BC$ is $\alpha_2$. If the length $DC$ remains constant for small changes in temperature,then:

Obtain the relation between the coefficient of volume expansion $(\alpha_V)$ and the coefficient of linear expansion $(\alpha_l)$.

$A$ metal ball initially at a pressure of $10^5 \ Pa$ is heated from $20^{\circ} C$ to $127^{\circ} C$ while keeping its volume constant. The coefficient of linear expansion of the metal is $10^{-5} \ {^{\circ} C}^{-1}$ and the bulk modulus of the metal is $2 \times 10^{11} \ N \ m^{-2}$. The final pressure inside the ball becomes:

$A$ blacksmith fixes a circular iron frame on the wooden wheel of a bullock cart. The diameters of the wooden wheel and the circular iron frame are $5.012 \ m$ and $5 \ m$ respectively at $27^{\circ} C$. The temperature (in $^{\circ} C$) to which the iron ring must be heated so as to fit the wooden wheel is (Coefficient of linear expansion of iron $= 1.2 \times 10^{-5} \ ^{\circ} C^{-1}$).

The volume of a metal sphere increases by $0.33 \%$ when its temperature is raised by $50^{\circ} C$. The coefficient of linear expansion of the metal is