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

For an ideal gas, the mean squared velocity \( \langle v^2 \rangle \) is related to the temperature by the equation: \[ \langle v^2 \rangle = \frac{3kT}{m} \] where \( k \) is the Boltzmann constant, \( T \) is the temperature, and \( m \) is the mass of the gas molecules. 

Step 1: The equation shows a linear relationship between mean squared velocity and temperature. 

Step 2: Therefore, the correct graph is a straight line with a positive slope. 

Final Conclusion: The graph representing a linear variation of mean squared velocity with temperature corresponds to Option (3).