The statement "The coefficient of linear expansion of iron is 0.000012 K⁻¹" (or 1.2 × 10⁻⁵ K⁻¹) provides information about how the length of an iron object changes with temperature.
Here’s what it means in detail:
1. **Coefficient of Linear Expansion (α)**: This is a material-specific value that measures the fractional change in length per degree change in temperature.
2. **Numerical Value (0.000012 K⁻¹)**: This indicates that for each degree Kelvin (or Celsius) change in temperature, the length of an iron object will change by 0.000012 times its original length.
3. **Unit (K⁻¹)**: This means the change is measured per Kelvin (or Celsius), as both scales have the same interval size.
### Explanation with Example:
Suppose you have an iron rod that is 1 meter (1000 mm) long at a certain initial temperature, \( T_0 \).
- If the temperature increases by 1 K (or 1°C), the change in length \( ΔL \) can be calculated as:
\[
ΔL = L_0 \cdot α \cdot ΔT
\]
Where \( L_0 \) is the original length, \( α \) is the coefficient of linear expansion, and \( ΔT \) is the change in temperature.
- For \( L_0 = 1 \) meter (1000 mm),
- \( α = 0.000012 \text{ K}^{-1} \),
- \( ΔT = 1 \text{ K} \),
we get:
\[
ΔL = 1 \text{ m} \cdot 0.000012 \text{ K}^{-1} \cdot 1 \text{ K} = 0.000012 \text{ m} \text{ (or 0.012 mm)}
\]
So, if the temperature of the iron rod increases by 1 Kelvin (or 1 degree Celsius), its length will increase by 0.000012 meters (or 0.012 millimeters).
Likewise, if the temperature decreases by 1 Kelvin (or 1 degree Celsius), its length will decrease by 0.000012 meters (or 0.012 millimeters).
### Summary:
The coefficient of linear expansion of iron being 0.000012 K⁻¹ means that the length of an iron object will proportionally expand or contract by 0.000012 times its original length for each degree increase or decrease in temperature. This property is crucial in engineering and materials science for designing structures and components that will undergo thermal variations.
8. The coefficient of linear expansion of iron is 0.000012K-1
(c) Explain the meaning of this statement
1 answer