The curve between absolute temperature and `v_(rms)^(2)` is

Options

A.
B.
C.
D.

Explanation

To find the relationship between absolute temperature (T) and the square of the root mean square speed (v_rms²), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of v_rms**:
The root mean square speed (v_rms) of gas molecules is given by the formula:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]
where R is the universal gas constant, T is the absolute temperature, and M is the molar mass of the gas.

2. **Square the v_rms Expression**:
To find the relationship between v_rms² and T, we square both sides of the equation:
\[ v_{rms}^2 = \frac{3RT}{M} \]

3. **Identify the Relationship**:
From the equation \( v_{rms}^2 = \frac{3RT}{M} \), we can see that v_rms² is directly proportional to T. This can be expressed as:
\[ v_{rms}^2 \propto T \]

4. **Conclusion about the Curve**:
Since v_rms² is directly proportional to T, we can conclude that if we plot v_rms² against T, the graph will be a straight line passing through the origin. This indicates a linear relationship.

5. **Final Answer**:
Therefore, the curve between absolute temperature (T) and v_rms² is a straight line.