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What is the R.M.S. velocity of gas molecules at temperature T2 = 127°C if V1 = 200 m/s at T1 = 27°C?

1. V2 = √(400/300)
2. V2 = 200 × √(2)
3. V2 = 400/√3
4. V2 = 200 × √(3)

Correct answer: V2 = 200 × √(2)

Solution

The R.M.S. velocity of gas molecules is proportional to the square root of the absolute temperature. Converting temperatures to Kelvin, T1 = 300 K and T2 = 400 K. Using the relation V2 = V1 × √(T2/T1), we get V2 = 200 × √(400/300) = 200 × √(4/3) = 200 × √(2).

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