Problem 3: Volume Expansion A cubic material has a coefficient of linear expansion of 12 x 10=% /2. If the side length of the material at 20C is 10 cm, calculate the new side length when the temperature is increased to 60C. Solution 1. Calculate the change in temperature: AT = 60 20. 2. Apply the linear expansion formula: AL = LyoAT. 3. Find the new length: L = Ly + AL Problem 4: Elastic Modulus and Stress-Strain A eylindrical steel rod with a diameter of 10 mm and a length of 2 m is subjected to a tensile force, cansing it to stretch by 1 mm. Caleulate the stress and strain on the rod. Verify if the stress matches the stress obtained from the Young's modulus equation. Solution 1. Caleulate the original cross-sectional area A of the rod. 2. Determine the strain using the change in length and original length. 3. Calculate the stress o using the force and original area. 4. Verify using Young's modulus: E = . Problem 5: Diffusion Coefficient The diffusion coefficient (DY) of carbon in iron at 1000C is 1.2 x 10 m? /5. Calculate the diffusion coefficient at 1100C using the Arrhenius equation. Solution 1. Use the Arrhenius equation: D = D'(.E_;'?'. 2. Solve for Dy using the given data at 1000C. 3. Caleulate D at 1100C using the same Dy and (1