Q.A sample of ideal gas is at equilibrium. Which of the following quantity is zero?

Definition and formula. The mean (or average) speed, $\bar v$, is the plain arithmetic average of every individual molecule's speed in the gas -- unlike $v_{rms}$, it averages the speeds directly rather than averaging their squares first. Derived from the Maxwell speed distribution function, its formula is

Where it sits among the three speeds. Because $1.60<1.73$, $\bar v$ is always smaller than $v_{rms}$ for the same gas at the same temperature -- specifically, $\bar v\approx0.92\,v_{rms}$. This is a genuinely important distinction: many students instinctively confuse 'root mean square speed' with a simple 'average speed', but the two are conceptually different averaging procedures over the same underlying speed distribution, and they give numerically different (though closely related) answers. …