Which of the following statements is/are true?

Options

A. The ratio of the mean speed to the rms speed is independent of the temperature.
B. Square of the mean speed of the molecules is equal to the square of the rms speed at a certain temperature.
C. Mean kinetic energy of the gas molecules at any given temperature is independent of the mean speed.
D. The difference between the rms speed and the mean speed at any temperature for different gases diminishes as larger, and yet larger molar masses are considered.

Explanation

To determine which statements are true, we will analyze each statement one by one based on the principles of kinetic theory and gas laws.

### Step-by-Step Solution:

1. **Statement 1: The ratio of the mean speed to the RMS speed is independent of the temperature.**
- **Mean Speed (v̄)**: \( v̄ = \sqrt{\frac{8RT}{\pi m}} \)
- **RMS Speed (v_rms)**: \( v_{rms} = \sqrt{\frac{3RT}{M}} \)
- **Ratio**:
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