Q20 / 120 · VITEEE 2013 · Chemistry
When 1 mole of $\mathrm{CO}_{2}(\mathrm{~g})$ occupying volume $10 \mathrm{~L}$ at $27^{\circ} \mathrm{C}$ is expanded under adiabatic condition, temperature falls to $150 \mathrm{~K}$. Hence,final volume is
- A$5 \mathrm{~L}$
- B$20 \mathrm{~L}$
- C$40 \mathrm{~L}$
- Correct answerD$80 \mathrm{~L}$
Solution
In adiabatic expansion
$\frac{T_{2}}{T_{1}}=\left(\frac{V_{1}}{V_{2}}\right)^{\gamma-1}$
for $\mathrm{CO}_{2}$ (triatomic gas) is,
$\begin{array}{l}
\therefore\left(\frac{150}{300}\right)=\left(\frac{10}{\mathrm{~V}_{2}}\right)^{0.33} \\
\left(\frac{1}{2}\right)=\left(\frac{10}{\mathrm{~V}_{2}}\right)^{0.33} \\
\left(\frac{1}{2}\right)^{3}=\frac{10}{\mathrm{~V}_{2}} \\
\frac{1}{8}=\frac{10}{\mathrm{~V}_{2}} \\
\mathrm{~V}_{2}=80 \mathrm{~L}
\end{array}$
Hence, the correct answer is option: 'D'.