A metal rod of length 1 m expands by 0.02 m when heated from 20°C to 120°C. Calculate its coefficient of linear expansion.

Solution & explanation

1. Given: L₀ = 1 m, ΔL = 0.02 m, T₁ = 20°C, T₂ = 120°C.

2. Find: α in K⁻¹.

3. Subtract the initial temperature from the final. A Celsius interval equals a kelvin interval.

   $${\Delta }_T=120-20=100$$

4. Write the linear expansion equation.

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

5. Divide both sides by L₀ΔT.

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

6. Substitute the values.

   $$\alpha =\frac{0.02}{1\times 100}$$

7. Multiply the denominator, then divide.

   $$\alpha =\frac{0.02}{100}=0.0002$$

8. State the result with units: 2.0×10⁻⁴ K⁻¹.

α = 2.0×10⁻⁴ K⁻¹