The root-mean-square speed (thermal speed)of the molecules of a gas is 200 m/s at 23.0°C.At 227°C the root-mean-square speed (thermal speed)of the molecules will be closest to
A) 160 m/s.
B) 330 m/s.
C) 260 m/s.
D) 630 m/s.
E) 2000 m/s.

Question

Quizplus · Accepted Answer

The root-mean-square speed of gas molecules is directly proportional to the square root of absolute temperature.
Thus, we can use the equation: 
(u2/u1) = sqrt(T2/T1)
where u is the root-mean-square speed and T is the absolute temperature.
Plugging in the given values, we get:
(u2/200m/s) = sqrt((273+227)K/(273+23)K)
(u2/200m/s) = sqrt(500/296)
u2 = 260 m/s (approx)
Therefore, the closest answer choice is C: 260 m/s.

The Root-Mean-Square Speed (Thermal Speed)of the Molecules of a Gas