The change in length of the rod when it is heated is given by the equation:

$\Delta L = L_0 \cdot \alpha \cdot \Delta T$

where

• $\Delta L$ is the change in length,
• $L_0$ is the original length,
• $\alpha$ is the coefficient of linear expansion, and
• $\Delta T$ is the change in temperature.

Substituting the given values:

$\Delta L = 1 \, \text{m} \cdot 10^{-5} \, \text{K}^{-1} \cdot 200 \, \text{K} = 0.002 \, \text{m}$

The rod is not allowed to extend or bend, so a stress is created in the rod. This stress can be calculated using Young's modulus (Y), which is the ratio of the stress (force per unit area, F/A) to the strain (change in length per unit length, $\Delta L / L_0$):

$Y = \frac{F/A}{\Delta L / L_0}$

Rearranging for F gives:

$F = Y \cdot A \cdot \frac{\Delta L}{L_0}$

Substituting the given values:

$F = 2 \times 10^{11} \, \text{N/m}^2 \cdot 10^{-4} \, \text{m}^2 \cdot \frac{0.002 \, \text{m}}{1 \, \text{m}} = 4 \times 10^{4} \, \text{N}$

So the compressive tension produced in the rod is $4 \times 10^{4} \, \text{N}$.