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 regarding Maxwell's speed distribution, we need to analyze the statements provided and determine which one is incorrect. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand Maxwell's Speed Distribution
Maxwell's speed distribution describes the distribution of speeds of particles in a gas. The curve is not symmetrical and has a specific shape that indicates the most probable speed, average speed, and root mean square speed of the gas molecules.

### Step 2: Review the Statements
We have four statements to evaluate:
1. The distribution function depends only on the absolute temperature.
2. Vrms is greater than Vaverage and Vmost prevalent is the lowest.
3. The area under the distribution curve gives the total number of molecules of gas.
4. The distribution curve is symmetric about the most prevalent speed.

### Step 3: Evaluate Each Statement
- **Statement 1**: This is correct. The distribution function does depend on the absolute temperature, as changing the temperature alters the shape of the curve.

- **Statement 2**: This is also correct. In Maxwell's distribution, the relationship is such that Vrms > Vaverage > Vmost prevalent speed.

- **Statement 3**: This statement is correct as well. The area under the curve represents the total number of molecules in the gas.

- **Statement 4**: This statement is incorrect. The distribution curve is not symmetric about the most prevalent speed; it is skewed to the right, indicating that there are more molecules with higher speeds.

### Step 4: Identify the Incorrect Statement
From the evaluations, we find that **Statement 4** is the incorrect one.

### Conclusion
The incorrect statement about Maxwell's speed distribution is: **The distribution curve is symmetric about the most prevalent speed.**

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