Which one of the following statement is not true about the effect of an increase in temperature on the distribution of molecular speed of gas ? .

Options

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

Explanation

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

### Step 1: Understand the Concept of 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 gas molecules vary at a given temperature.

**Hint:** Recall that the Maxwell-Boltzmann distribution illustrates the relationship between temperature and molecular speed.

### Step 2: Analyze the Statements
We have four statements regarding the effect of temperature on the molecular speed distribution. We need to determine which one is not true.

1. **Most Probable Speed Increases**: This statement is true. As the temperature increases, the most probable speed (V_mp) of the gas molecules increases.

**Hint:** Remember that the most probable speed is the speed at which the maximum number of molecules are found.

2. **Fraction of Molecules with Most Probable Speed Increases**: This statement is not true. As temperature increases, the fraction of molecules that have the most probable speed actually decreases. The distribution broadens, meaning fewer molecules are at the most probable speed.

**Hint:** Consider how the shape of the distribution curve changes with temperature.

3. **Distribution Becomes Broader**: This statement is true. With an increase in temperature, the distribution of molecular speeds becomes broader, indicating a wider range of speeds among the molecules.

**Hint:** Visualize how the graph of the distribution looks at different temperatures.

4. **Area Under Distribution Curve Remains the Same**: This statement is true. The area under the curve represents the total number of molecules, which remains constant regardless of temperature changes.

**Hint:** Think about the conservation of the number of molecules in a closed system.

### Step 3: Conclusion
After analyzing all the statements, the statement that is not true is the second one: "The fraction of molecules with the most probable speed increases."

**Final Answer:** The statement that is not true is **B**.

### Summary of Steps
1. Understand the concept of molecular speed distribution.
2. Analyze each statement regarding the effects of temperature.
3. Conclude which statement is not true based on the analysis.