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The temperature of a gas is raised from 27°C to 927°C. The root mean square speed is

1. √(927/27) times the earlier value
2. remain the same
3. gets halved
4. get doubled

Correct answer: get doubled

Solution

The root mean square (RMS) speed of gas molecules is proportional to the square root of the absolute temperature (Kelvin). Converting the given temperatures to Kelvin (27°C = 300 K, 927°C = 1200 K), the ratio of RMS speeds is √(1200/300) = √4 = 2. Thus, the RMS speed gets doubled.

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