A 1.5 m metal rod expands by 0.025 m when heated from 30°C to 180°C. Calculate its coefficient of linear expansion.

Solution & explanation

1. Given: initial length 1.5 m; increase 0.025 m; initial and final temperatures 30°C and 180°C.

2. Subtract temperatures; a temperature interval in °C has the same numerical value in K.

   $${\Delta }_T=180-30=150$$

3. Write the expansion equation.

   $${\Delta }_L={\Delta }_T\times L_0\times \alpha$$

4. Divide by initial length times temperature rise.

   $$\alpha =\frac{{\Delta }_L}{{\Delta }_T\times L_0}$$

5. Substitute in metres and kelvin.

   $$\alpha =\frac{0.025}{1.5\times 150}$$

6. Multiply the denominator.

   $$\alpha =\frac{0.025}{225}$$

7. Divide and round appropriately.

   $$\alpha =0.000111111111111$$

α ≈ 1.11 × 10⁻⁴ K⁻¹