An external pressure $P$ is applied on a cube at $0^o C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and a is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by

What is areal expansion ? Give definition and unit of coefficient of areal expansion.

A copper rod of $88\; \mathrm{cm}$ and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of aluminum rod is....$cm$

$( \alpha_{Cu}=1.7 \times 10^{-5}\; \mathrm{K}^{-1}$ and $\alpha_{Al}=2.2 \times 10^{-5} \;\mathrm{K}^{-1} ) $

Two rods $A$ and $B$ of identical dimensions are at temperature $30\,^oC$. If a heated upto $180\,^oC$ and $B$ upto $T\,^oC$, then the new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is $4:3$, then the value of $T$ is........$^oC$

A solid metallic cube having total surface area $24\;m ^{2}$ is uniformly heated. If its temperature is increased by $10\,^{\circ} C$, calculate the increase in volume of the cube $\left(\right.$ Given $\left.: \alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)$

Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be

( ${\alpha _1},\,{\alpha _2},$ = linear expansion coefficient

$A_1, A_2$ = Area of rods

$Y_1, Y_2$ = Young modulus)