For a particular ideal gas, which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?
Show Hint
The Correct Option is C
Solution and Explanation
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).
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