Question

The temperature of an ideal gas is increased from $27$ ${}^{o}C$ to $127$ ${}^{o}C$, then percentage increase in $v_{rms}$ is?

• A. $37\%$
• B. $11\%$
• C. $33\%$
• D. $15.5\%$

Answer 1

Answer: (D)

$15.5\%$

$v_{rms}=\sqrt{\frac{3RT}{M}}$
$\%$ increase in $v_{rms}=\frac{\sqrt{\frac{3R{T}_2}{M}}-\sqrt{\frac{3R{T}_1}{M}}}{\sqrt{\frac{3R{T}_1}{M}}}$ $\times 100$
$=\frac{\sqrt{T_2}-\sqrt{T_1}}{\sqrt{T_1}}\times 100=\frac{\sqrt{400}-\sqrt{300}}{\sqrt{300}}\times 100$
$=\frac{20-17.32}{17.32}\times 100=15.5\%$