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 proportional to the temperature \( T \), according to the equation: \[ \langle v^2 \rangle = \frac{3k}{m} T \] where \( k \) is the Boltzmann constant and \( m \) is the mass of the gas molecules. Analysis: The equation \( \langle v^2 \rangle = (\frac{3k}{m}) T \) indicates a direct linear relationship between the mean squared velocity and the temperature, with the constant of proportionality being \( \frac{3k}{m} \). Conclusion: A graph illustrating a linear relationship between mean squared velocity and temperature should be a straight line passing through the origin with a positive slope. This corresponds to Option (3).