Question

For an ideal gas of molar mass \( M \), the slope of the graph between the rms speed \( V \) and \( \sqrt{T} \) where \( T \) represents the temperature is...

• A. \( \frac{1}{\sqrt{M}} \)
• B. \( \frac{1}{M} \)
• C. \( \sqrt{M} \)
• D. \( M \)

Hint:

The rms speed of an ideal gas is directly proportional to the square root of the temperature and inversely proportional to the square root of the molar mass.

Answer 1

The Correct Option is A

For an ideal gas, the root mean square (rms) speed is related to temperature \( T \) by the equation: \[ V_{\text{rms}} = \sqrt{\frac{3kT}{M}} \] where \( k \) is Boltzmann constant and \( M \) is the molar mass. The slope of the graph between \( V_{\text{rms}} \) and \( \sqrt{T} \) is proportional to \( \frac{1}{\sqrt{M}} \).