Question

The molecules in an ideal gas at $27^{\circ} C$ have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled?

• A. $54^{\circ} C$
• B. $327^{\circ} C$
• C. $1200^{\circ} C$
• D. $927^{\circ} C$

Answer 1

Answer: (D)

$927^{\circ} C$

Answer 2

Mean velocity of gas molecules
$v=\sqrt{\frac{8 R T}{\pi T}}$
$v \propto \sqrt{T}$
$\frac{v_{1}}{v_{2}}=\sqrt{\frac{T_{1}}{T_{2}}}$
$\frac{v_{1}}{v_{2}}=\sqrt{\frac{300}{T_{2}}}$
$\frac{v_{1}}{2 v_{1}}=\sqrt{\frac{300}{T_{2}}}$
$\frac{1}{4}=\frac{300}{T_{2}}$
$T_{2}=1200$
$K=1200-273$
$=927^{\circ} C$