The root mean square (rms) speed of the molecules of an ideal gas at a given temperature \(T\) is \(v\). If the temperature is increased to \(4T\) and the gas dissociates into atoms, the new rms speed becomes:
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Don't forget to track the mass variable when a problem explicitly mentions "dissociation"! Dissociation always drops the particle weight by half (or more depending on the chemical complexity), which simultaneously accelerates the speed of the individual particles alongside the temperature expansion.