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 determine 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 material changes with temperature. For most materials, including copper, this coefficient can vary with temperature.

### Step 2: Analyze the Behavior of Volume Expansion with Temperature
- At lower temperatures, the volume expansion of copper is generally linear. This means that as the temperature increases, the volume expands in a predictable, linear manner.
- As the temperature continues to rise, the behavior of volume expansion becomes non-linear. This means that the rate of expansion increases at higher temperatures.
- After reaching a certain temperature, the coefficient of volume expansion may become constant, indicating that further increases in temperature do not significantly affect the volume expansion.

### Step 3: Examine the Given Graphs
We need to look for a graph that:
- Starts with a linear increase in the coefficient of volume expansion at lower temperatures.
- Transitions to a non-linear increase as the temperature rises.
- Levels off and becomes constant after reaching a certain temperature.

### Step 4: Identify the Correct Graph
Based on the characteristics described:
- The correct graph should show an initial linear increase followed by a non-linear increase, and then a plateau indicating a constant value after a certain temperature.

From the options provided, we find that **Option C** meets these criteria:
- Initially linear increase.
- Followed by a non-linear increase.
- Finally, a constant value after a specific temperature.

### Conclusion
The correct option that represents the variation of the coefficient of volume expansion of copper as a function of temperature is **Option C**.

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