Search any question & find its solution
Question:
Answered & Verified by Expert
The temperature of an ideal gas is increased from $27^{\circ} \mathrm{C}$ to $127^{\circ} \mathrm{C}$, then percentage increase in $\mathrm{v}_{\mathrm{rms}}$
is
Options:
is
Solution:
1813 Upvotes
Verified Answer
The correct answer is:
$15.5 \%$
We know, $\mathrm{V}_{\mathrm{mms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$
$\Rightarrow \%$ increase in
$$
\begin{array}{l}
\mathrm{V}_{\mathrm{rms}}=\frac{\sqrt{\frac{3 \mathrm{R} \mathrm{T}_{2}}{\mathrm{M}}}-\sqrt{\frac{3 \mathrm{RT}_{1}}{\mathrm{M}}}}{\sqrt{\frac{3 \mathrm{RT}_{1}}{\mathrm{M}}}} \times 100 \\
=\frac{\sqrt{\mathrm{T}_{2}}-\sqrt{\mathrm{T}_{1}}}{\sqrt{\mathrm{T}_{1}}} \times 100 \\
=\frac{\sqrt{400}-\sqrt{300}}{\sqrt{300}} \times 100 \\
=\frac{20-17.32}{17.32} \times 100=15.5 \%
\end{array}
$$
$\Rightarrow \%$ increase in
$$
\begin{array}{l}
\mathrm{V}_{\mathrm{rms}}=\frac{\sqrt{\frac{3 \mathrm{R} \mathrm{T}_{2}}{\mathrm{M}}}-\sqrt{\frac{3 \mathrm{RT}_{1}}{\mathrm{M}}}}{\sqrt{\frac{3 \mathrm{RT}_{1}}{\mathrm{M}}}} \times 100 \\
=\frac{\sqrt{\mathrm{T}_{2}}-\sqrt{\mathrm{T}_{1}}}{\sqrt{\mathrm{T}_{1}}} \times 100 \\
=\frac{\sqrt{400}-\sqrt{300}}{\sqrt{300}} \times 100 \\
=\frac{20-17.32}{17.32} \times 100=15.5 \%
\end{array}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.