$(25$p$)$

${}_1=16*{10}^{-6}\frac{1}{C^O}$

${}_2=12*{10}^{-6}\frac{1}{C^o}$

$E_1=100$GPa

$E_2=200$GPa

${}_{\text{a}\text{l}\text{l}\text{o}\text{w}1}=100$MPa

${}_{\text{a}\text{l}\text{l}\text{o}\text{w}2}=150$MPa

In the figure, a circular cross$-$section rod with a diameter of $4cm,$ made of material with

number $1,$ is placed inside the pipe produced from material with number $2.$ The entire

system is mounted on a rigid plate from below and on a fixed wall from above. The

temperature when the system is installed is $10C.$ How much should the temperature be

changed to close the $0\mathrm{.}023cm$ gap?