Question

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

• A. ${200}^{\circ }$C
  
• B. ${273}^{\circ }$C
  
• C. ${1219}^{\circ }$C
  
• D. ${1492}^{\circ }$C

Answer 1

The correct option is C

${1219}^{\circ }$C

$V_{rms}\propto \sqrt{T}$
${100}^{\circ }$C $=373$K
For $V_{rms}$ to get doubled, $T$ has to be increased four times.
Hence, at $4$ times $373K$ $=1492K={1219}^{\circ }$ C, $V_{rms}$ gets doubled.