Which of the following graphs correctly shows variation of coefficient of volume expansion of copper as a function of temperature ?

Options

A.
B.
C.
D.

Answer

To solve the problem of determining which graph correctly shows the variation of the coefficient of volume expansion of copper as a function of temperature, we can follow these steps:

### Step 1: Understand the Concept of Volume Expansion
The coefficient of volume expansion (β) describes how the volume of a substance changes with temperature. For solids like copper, this coefficient can change with temperature.

### Step 2: Analyze the Relationship
The relationship for volume expansion can be expressed as:
\[ \frac{\Delta V}{V} = \beta \Delta T \]
Where:
- \(\Delta V\) is the change in volume,
- \(V\) is the original volume,
- \(\beta\) is the coefficient of volume expansion,
- \(\Delta T\) is the change in temperature.

### Step 3: Consider the Temperature Dependence
As temperature increases, the coefficient of volume expansion for materials like copper typically increases initially and may reach a point where it becomes relatively constant. This means that the graph will not be a straight line but will show a nonlinear increase initially and then level off.

### Step 4: Evaluate the Graph Options
Now we need to evaluate the four graph options given:
1. **Option 1**: Shows a nonlinear increase but does not level off.
2. **Option 2**: Also shows a nonlinear increase without leveling off.
3. **Option 3**: Shows a nonlinear increase initially and then becomes constant after a certain temperature.
4. **Option 4**: Shows a linear increase, which is incorrect for this scenario.

### Step 5: Identify the Correct Graph
From the analysis:
- **Option 3** is the correct graph as it accurately represents the behavior of the coefficient of volume expansion of copper, showing an initial nonlinear increase followed by a constant value.

### Conclusion
The correct answer is **Option 3**.

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