Which one of the following statements is not true about the effect of an increase in temperature on the distribution of molecular speeds in a gas?

Options

A. The area under the distribution curve remains the same as under the lower temperature.
B. The distribution becomes broader.
C. The fraction of the molecules with the most probable speed increases.
D. The most probable speed increases.

Explanation

To solve the question regarding the effect of an increase in temperature on the distribution of molecular speeds in a gas, we can analyze the provided statements step by step.

### Step-by-Step Solution:

1. **Understanding Molecular Speed Distribution**:
- The distribution of molecular speeds in a gas is described by the Maxwell-Boltzmann distribution. This distribution shows how the speeds of molecules in a gas vary at a given temperature.

2. **Effect of Temperature on the Distribution**:
- As the temperature of a gas increases, the average kinetic energy of the molecules also increases. This leads to an increase in the speeds of the gas molecules.

3. **Plotting the Distribution Curves**:
- When we plot the distribution of molecular speeds at two different temperatures (T1 and T2, where T2 > T1), we observe that the curve for T2 is shifted to the right compared to T1. This indicates that at a higher temperature, molecules have higher speeds.

4. **Analyzing the Statements**:
- **Statement A**: "The area under the distribution curve remains the same as under the lower temperature."
- This statement is true because the area under the curve represents the total number of molecules, which does not change with temperature.

- **Statement B**: "The distribution becomes broader."
- This statement is also true. As temperature increases, the distribution becomes broader and the peak of the curve shifts to the right, indicating a wider range of molecular speeds.

- **Statement C**: "The fraction of the molecules with the most probable speed increases."
- This statement is **not true**. As temperature increases, while the most probable speed increases, the fraction of molecules at that most probable speed actually decreases. The peak of the distribution curve at higher temperatures is lower than that at lower temperatures, indicating fewer molecules have the most probable speed.

- **Statement D**: "The most probable speed increases."
- This statement is true. The most probable speed is directly proportional to the square root of the temperature, so as temperature increases, the most probable speed also increases.

5. **Conclusion**:
- The statement that is **not true** regarding the effect of an increase in temperature on the distribution of molecular speeds in a gas is **Statement C**.

### Final Answer:
**The correct answer is Statement C: "The fraction of the molecules with the most probable speed increases."**