Question

For a particular ideal gas, which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

• A.
• B.
• C.
• D.

Hint:

Remember that in ideal gases, the mean squared velocity is directly proportional to temperature.

Answer 1

The Correct Option is C

The mean squared velocity \( \langle v^2 \rangle \) of an ideal gas is expressed as \( \langle v^2 \rangle = \frac{3kT}{m} \), where \( k \) is the Boltzmann constant, \( T \) is the temperature, and \( m \) is the mass of the gas molecules.

Step 1: This equation indicates a direct proportionality between mean squared velocity and temperature.

Step 2: Consequently, the appropriate graphical representation is a straight line exhibiting a positive gradient.

Final Conclusion: The graph depicting a linear correlation between mean squared velocity and temperature aligns with Option (3).