Question

The temperature of an ideal gas is increased from $27^{\circ} C$ to $127^{\circ} C$, then percentage increase in $v_{r m s}$ is

• A. 37%
• B. 0.11
• C. 0.33
• D. 0.155

Answer 1

Answer: (D)

0.155

Answer 2

$v _{ rms }=\sqrt{\frac{3 RT }{ M }}$ $\%$ increase in $v _{ rms }=\frac{\sqrt{\frac{3 RT _{2}}{ M }}-\sqrt{\frac{3 RT _{1}}{ M }}}{\sqrt{\frac{3 RT _{1}}{ M }}} \times 100$ $=\frac{\sqrt{ T _{2}}-\sqrt{ T _{1}}}{\sqrt{ T _{1}}} \times 100$ $=\frac{\sqrt{400}-\sqrt{300}}{\sqrt{300}} \times 100$ $=\frac{20-17.32}{17.32} \times 100$ $=15.5 \%$