When the temperature of a copper coin is raised by `80^@C`, its diameter increases by `0.2%`.

Options

A. percentage rise in the area of a face is `0.4%`
B. percentage rise in the thickness is `0.4%`
C. percentage rise in the volume is `0.6%`
D. corfficient of linear expansion of copper is `0.25xx10^(-4)//^(@)C`

Explanation

To solve the problem, we need to find the coefficient of linear expansion (α) of copper given that the diameter of a copper coin increases by 0.2% when the temperature is raised by 80°C.

### Step-by-Step Solution:

1. **Understand the relationship between linear expansion and temperature change**:
The formula for linear expansion is given by:
\[ \frac{\Delta L}{L} = \alpha \Delta T \]
where:
- \(\Delta L\) = change in length (or diameter in this case)
- \(L\) = original length (or diameter)
- \(\alpha\) = coefficient of linear expansion
- \(\Delta T\) = change in temperature

2. **Convert the percentage change in diameter to a decimal**:
The diameter increases by 0.2%, which can be expressed as:
\[ \frac{\Delta L}{L} = \frac{0.2}{100} = 0.002 \]

3. **Identify the change in temperature**:
The temperature change is given as:
\[ \Delta T = 80^\circ C \]

4. **Substitute the values into the linear expansion formula**:
We can now substitute the values into the formula:
\[ 0.002 = \alpha \times 80 \]

5. **Solve for α**:
Rearranging the equation to solve for α gives:
\[ \alpha = \frac{0.002}{80} \]

6. **Calculate α**:
Performing the calculation:
\[ \alpha = \frac{0.002}{80} = 0.000025 = 2.5 \times 10^{-5} \, \text{per} \, ^\circ C \]

### Final Answer:
The coefficient of linear expansion of copper is:
\[ \alpha = 2.5 \times 10^{-5} \, \text{per} \, ^\circ C \]