In the given figure, a circular cross

$-$

section rod with a diameter of

$4$

$$cm made of material

$1$

$$is inserted into the pipe made of material

$2.$

$$

The whole system is supported from the bottom by a rigid

plate and top mounted on a fixed wall. The temperature at the time the system is installed is

$10$

$\backslash$

deg C

$.$

$$How much must the temperature be changed to close the

$0\mathrm{.}013$

$$cm gap?