A copper bar is 80 cm long at `15^(@)C`. What is the increase in length, when heated to `35^(@)C`? The coefficient of linear expansion for copper is `1.7 xx 10^(-5).^(@)C^(-1)`

Answer

To find the increase in length of the copper bar when heated from \(15^\circ C\) to \(35^\circ C\), we can use the formula for linear expansion:

\[ \Delta L = L_0 \cdot \alpha \cdot \Delta T \]

Where:
- \(\Delta L\) is the change in length,
- \(L_0\) is the original length of the bar,
- \(\alpha\) is the coefficient of linear expansion,
- \(\Delta T\) is the change in temperature.

### Step 1: Identify the values
- Original length (\(L_0\)) = 80 cm = 0.80 m (convert to meters for standard SI units)
- Coefficient of linear expansion (\(\alpha\)) = \(1.7 \times 10^{-5} \, ^\circ C^{-1}\)
- Initial temperature = \(15^\circ C\)
- Final temperature = \(35^\circ C\)

### Step 2: Calculate the change in temperature (\(\Delta T\))
\[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 35^\circ C - 15^\circ C = 20^\circ C \]

### Step 3: Substitute the values into the formula
\[ \Delta L = L_0 \cdot \alpha \cdot \Delta T \]
\[ \Delta L = 0.80 \, \text{m} \cdot (1.7 \times 10^{-5} \, ^\circ C^{-1}) \cdot (20 \, ^\circ C) \]

### Step 4: Perform the calculation
\[ \Delta L = 0.80 \cdot 1.7 \times 10^{-5} \cdot 20 \]
\[ \Delta L = 0.80 \cdot 34 \times 10^{-5} \]
\[ \Delta L = 27.2 \times 10^{-5} \, \text{m} \]
\[ \Delta L = 0.000272 \, \text{m} = 0.0272 \, \text{cm} \]

### Final Answer
The increase in length of the copper bar when heated from \(15^\circ C\) to \(35^\circ C\) is \(0.0272 \, \text{cm}\).