Graph for specific heat at constant volume for a monoatomic gas

Options

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Answer

To solve the question regarding the graph for specific heat at constant volume (C_V) for a monoatomic gas, we can follow these steps:

### Step 1: Understand the Formula
The specific heat at constant volume for a monoatomic gas is given by the formula:
\[ C_V = \frac{3}{2} R \]
where \( R \) is the universal gas constant.

### Step 2: Analyze Independence from Temperature
From the formula, we can see that \( C_V \) is a constant value for a monoatomic gas and does not depend on temperature. This means that regardless of the temperature changes, the specific heat at constant volume remains the same.

### Step 3: Graph Representation
Since \( C_V \) is constant, when we plot it against temperature (T), we will get a horizontal line. The y-axis will represent \( C_V \) and the x-axis will represent temperature (T). The line will be at the value \( \frac{3}{2} R \).

### Step 4: Identify the Correct Option
In the options provided, we need to identify which graph represents a constant value of \( C_V \) as temperature changes. The correct graph will be a horizontal line at the height of \( \frac{3}{2} R \).

### Conclusion
The graph for the specific heat at constant volume for a monoatomic gas is a horizontal line at the value of \( \frac{3}{2} R \), indicating that it is independent of temperature.