The graph between the `(velocity)^(2)` and temperature `T` of a gas is

Options

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Explanation

To determine the graph between the square of the velocity \((v^2)\) and the temperature \(T\) of a gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
We start with the relationship derived from the kinetic theory of gases. The velocity \(v\) of gas molecules is related to the temperature \(T\) of the gas. According to the kinetic theory, the average velocity of gas molecules is proportional to the square root of the absolute temperature.

2. **Using the Formula**:
The formula we can use is:
\[ v \propto \sqrt{T} \]
This means that the velocity \(v\) is directly proportional to the square root of the temperature \(T\).

3. **Squaring the Relationship**:
To find the relationship between \(v^2\) and \(T\), we square both sides of the equation:
\[ v^2 \propto T \]
This indicates that the square of the velocity is directly proportional to the temperature.

4. **Graph Interpretation**:
If we plot \(v^2\) on the y-axis and \(T\) on the x-axis, the relationship \(v^2 \propto T\) suggests that the graph will be a straight line. However, we must consider the behavior at \(T = 0\).

5. **Considering the Zero Temperature**:
At absolute zero temperature (\(T = 0\)), the velocity of gas molecules does not become zero due to quantum effects. Therefore, the graph will not pass through the origin. Instead, it will start from a positive value on the y-axis.

6. **Conclusion**:
Thus, the graph of \(v^2\) versus \(T\) will be a straight line that does not pass through the origin, indicating a linear relationship with a positive intercept.

### Final Answer:
The graph between \((velocity)^2\) and temperature \(T\) of a gas is a straight line that does not pass through the origin.

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