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

Options

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Explanation

To find the relationship between the square of the velocity (V²) of a gas and its temperature (T), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the RMS Velocity Formula**:
The root mean square (RMS) velocity of gas molecules is given by the formula:
\[ V_{rms} = \sqrt{\frac{3RT}{m}} \]
where \( R \) is the universal gas constant, \( T \) is the temperature, and \( m \) is the molecular weight of the gas.

**Hint**: Recall the definition of RMS velocity and the variables involved.

2. **Square the RMS Velocity**:
To find the relationship between V² and T, we square the RMS velocity:
\[ V^2 = \left(\sqrt{\frac{3RT}{m}}\right)^2 = \frac{3RT}{m} \]

**Hint**: Remember that squaring a square root cancels the square root.

3. **Identify the Proportionality**:
From the equation \( V^2 = \frac{3R}{m}T \), we can see that V² is directly proportional to T. The term \( \frac{3R}{m} \) is a constant.

**Hint**: Look for the relationship in the form of \( y = kx \) where \( k \) is a constant.

4. **Graphical Representation**:
Since V² is proportional to T, if we plot V² on the y-axis and T on the x-axis, the graph will be a straight line. This line will pass through the origin (0,0) because when T = 0, V² also equals 0.

**Hint**: Consider the characteristics of linear graphs and what it means for a line to pass through the origin.

5. **Conclusion**:
Therefore, the graph between the square of the velocity (V²) and temperature (T) of a gas is a straight line passing through the origin.

**Hint**: Summarize the findings to confirm the type of graph you expect.

### Final Answer:
The graph between the velocity squared (V²) and temperature (T) of a gas is a straight line passing through the origin.