Out of the following materials, whose elasticity is independent of temperature?

Options

A. Copper
B. Invar steel
C. Brass
D. Silver

Answer

To determine which material's elasticity is independent of temperature, we will analyze the coefficients of thermal expansion for each material provided: copper, inverse steel, brass, and silver.

### Step-by-Step Solution:

1. **Understanding Elasticity and Temperature Dependence**:
- Elasticity refers to the ability of a material to return to its original shape after deformation.
- The change in length (ΔL) of a material due to temperature change (ΔT) can be expressed as:
\[ \Delta L = L \cdot \alpha \cdot \Delta T \]
where \(L\) is the original length, and \(\alpha\) is the coefficient of linear expansion.

2. **Coefficients of Linear Expansion**:
- We need to find the coefficients of linear expansion (\(\alpha\)) for each material:
- Copper: \(\alpha = 17 \times 10^{-6} \, \text{K}^{-1}\)
- Inverse Steel: \(\alpha = 0.522 \times 10^{-6} \, \text{K}^{-1}\)
- Brass: \(\alpha = 20 \times 10^{-6} \, \text{K}^{-1}\)
- Silver: \(\alpha = 19.7 \times 10^{-6} \, \text{K}^{-1}\)

3. **Comparing Coefficients**:
- From the values obtained:
- Copper: \(17 \times 10^{-6}\)
- Inverse Steel: \(0.522 \times 10^{-6}\)
- Brass: \(20 \times 10^{-6}\)
- Silver: \(19.7 \times 10^{-6}\)
- The material with the lowest coefficient of linear expansion is inverse steel.

4. **Conclusion**:
- Since inverse steel has the lowest coefficient of thermal expansion, it will experience the least change in length with temperature variations. Therefore, its elasticity is approximately independent of temperature.

### Final Answer:
**Inverse Steel** is the material whose elasticity is independent of temperature.