Question

The rms speed of the gas at 300 K is 1370 m/s. What is its rms speed at 1200 K? Numeric Answer:

Answer 1

rms speed at 1200 K = 2740 m/s

Explanation

rms speed of a gas is directly proportional to square root of temperature

rms₂ / rms₁ = (T₂ / T₁)^1/2

where

rms₁ = rms speed at 300 K = 1370 m/s

T₁ = 300 K

rms₂ = rms speed at 1200 K

T₂ = 1200 K

Substituting the values

rms₂ / (1370 m/s) = (1200 K / 300 K)^1/2

rms₂ / (1370 m/s) = (4)^1/2

rms₂ / (1370 m/s) = 2

rms₂ = (1370 m/s) * 2

rms₂ = 2740 m/s