A steel rod is 2 m long at 20°C. Its linear-expansion coefficient is 1.2×10⁻⁵ °C⁻¹. Find its length at 100°C.

Solution & explanation

1. Given: L₀ = 2 m; α = 1.2×10⁻⁵ °C⁻¹.

2. Find the interval.

   $${\Delta }_T=100-20=80$$

3. Calculate the increase, not the final length yet.

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

4. Substitute in metres.

   $${\Delta }_L=\frac{192.0}{100000}$$

5. Multiply 2×80, then by the coefficient.

   $${\Delta }_L=0.00192$$

6. Add the initial length.

   $$L=0.00192+2=2.00192$$

7. State the result with units: 2.00192 m, about 2.002 m.

L = 2.00192 m ≈ 2.002 m