The pressure that has to be applied to the ends of a steel wire of length \(10~\text{cm}\) to keep its length constant when its temperature is raised by \(100^\circ \text{C}\) is:
(Young's modulus of steel is \(2\times 10^{11}~\text{Nm}^{-2}\) and coefficient of thermal expansion is \(1.1 \times 10^{-5}~\text{K}^{-1}\))
1. \( 2.2 \times 10^9 ~\text{Pa} \)
2. \( 2.2 \times 10^7 ~\text{Pa} \)
3. \( 2.2 \times 10^6 ~\text{Pa} \)
4. \( 2.2 \times 10^8 ~\text{Pa} \)

An external pressure \(P\) is applied on a cube at \(0^\circ\text{C}\) so that it is equally compressed from all sides. \(K\) is the bulk modulus of the material of the cube and \(\alpha\) 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:
1. \( \dfrac{{P}}{3 \alpha {K}}\)

2. \( \dfrac{{P}}{\alpha{K}} \)

3. \( \dfrac{3 \alpha}{{PK}} \)

4. \(3 {PK} \alpha\)

Given below are two statements: