Question

At what temperature would the rms speed of a gas molecule have twice its value at ${100}^{\circ }C$?

• A. $4192K$
• B. $1492K$
• C. $9142K$
• D. $2491K$

Answer 1

The correct option is B $1492K$

The rms speed (u) is directly proportional to the square root of temperature.

$\frac{u^{\prime }}{u}=\sqrt{\frac{T^{\prime }}{T}}$

$\frac{2u}{u}=\sqrt{\frac{T^{\prime }}{100+273}}$

$2=\sqrt{\frac{T^{\prime }}{373}}$

$4=\frac{T^{\prime }}{373}$

$T^{\prime }=1492K$

Thus, at 1492 K would the rms speed of a gas molecule have twice its value at 100 deg C