Question

Which of the following statements is (are) true?

• A. The ratio of the average speed to the rms speed is independent of the temperature
• B. The square of the mean squared speed of the molecule is equal to the mean square 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 rms speed and average speed at any temperature for different gases diminished as large molar masses are considered

Answer 1

Answer: (A), (C), (D)

The correct options are
A The ratio of the average speed to the rms speed is independent of the temperature
C Mean kinetic energy of the gas molecules at any given temperature is independent of the mean speed
D The difference between rms speed and average speed at any temperature for different gases diminished as large molar masses are considered

We know,

$U_{RMS}=\sqrt{\frac{3RT}{M}}$

$U_{avg}=\sqrt{\frac{8RT}{M}}$

$U_{MP}=\sqrt{\frac{2RT}{M}}$

Seeing these equations we can conclude that,

• The ratio of the average speed to the RMS speed is independent of the temperature.
• Mean kinetic energy of the gas molecules at any given temperature is independent of the mean speed.
  
• The difference between RMS speed and average speed at any temperature for different gases diminished as large molar masses are considered