Select the incorrect statement about Maxwell's speed distribution.

Options

A. The distribution function depends only on the absolute temperature
B. `V_("rms") gt V_("av") gt V_("mp")`
C. The area under the distribution curve gives total number of molecules of the gas
D. The distribution curve is symmetric about the most probable speed.

Answer

To solve the question of selecting the incorrect statement about Maxwell's speed distribution, we will analyze each statement one by one based on the information provided in the video transcript.

### Step-by-Step Solution:

1. **Statement 1: The distribution function depends on the absolute temperature.**
- The distribution function \( F(v) \) is given by the formula:
\[ F(v) = \frac{m}{2 \pi k T}^{\frac{3}{2}} e^{-\frac{mv^2}{2kT}} \]
- In this formula, \( T \) is the absolute temperature, and it is clear that the distribution function is indeed dependent on temperature. Thus, **Statement 1 is correct**.

2. **Statement 2: \( V_{rms} \) is greater than \( V_{average} \) is greater than \( V_{mostProbable} \).**
- The root mean square speed \( V_{rms} \), average speed \( V_{average} \), and most probable speed \( V_{mp} \) are defined as:
\[ V_{rms} = \sqrt{\frac{3kT}{m}}, \quad V_{average} = \sqrt{\frac{2kT}{m}}, \quad V_{mp} = \sqrt{\frac{8kT}{\pi m}} \]
- Comparing these values, we see that:
\[ V_{rms} > V_{average} > V_{mp} \]
- Therefore, **Statement 2 is correct**.

3. **Statement 3: The area under the distribution curve gives the total number of molecules of gas.**
- The area under the Maxwell distribution curve represents the total probability of finding all molecules at various speeds. Since the total probability must equal 1 for a normalized distribution, this statement is misleading. The area does not give the total number of molecules but rather the probability distribution. Thus, **Statement 3 is incorrect**.

4. **Statement 4: The distribution curve is symmetric about the most probable speed.**
- The Maxwell distribution curve is not symmetric about the most probable speed; it is skewed. The most probable speed is the peak of the distribution, and the distribution tails off on either side. Therefore, **Statement 4 is also incorrect**.

### Conclusion:
- The incorrect statements are **Statement 3** and **Statement 4**. However, since the question asks for a single incorrect statement, **Statement 3** is the most directly misleading regarding the interpretation of the area under the curve.

### Final Answer:
**The incorrect statement about Maxwell's speed distribution is Statement 3.**