Concept:The Kinetic Molecular Theory relates the macroscopic absolute temperature of a gas directly to the microscopic average speeds of its constituent molecules via the Root Mean Square (RMS) velocity.
Formula:$$ C_{rms} = \sqrt{\frac{3RT}{M}} $$
Solution:- In this equation, \( C_{rms} \) is the root mean square velocity, \( R \) is the universal gas constant, \( T \) is the absolute temperature in Kelvin, and \( M \) is the molar mass.
- This explicit formula defines how molecular velocity is directly proportional to the square root of the absolute temperature (\( C_{rms} \propto \sqrt{T} \)).
Why other options are incorrect:- Option B: The ideal gas law relates Pressure, Volume, and Temperature, but does not explicitly calculate molecular velocity.
- Option C: While mathematically true for classical kinetic energy, it does not directly incorporate the macroscopic "Absolute Temperature" (T) as requested by the prompt.
- Option D: The kinetic gas equation relates Pressure and Volume to mean square velocity, but does not explicitly contain Temperature (T).
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