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Q.
When $1 \,$ mole of $CO_{2(g)}$ occupying volume $10\,L$ at $27^{\circ}C$ is expanded under adiabatic condition, temperature falls to $150\, K$. Hence, final volume is
For adiabatic expansion
$\frac{T_{2}}{T_{1}}=\left(\frac{V_{1}}{V_{2}}\right)^{\gamma-1}$
Here, for $CO _{2}$ (triatomic gas),
$\gamma=1.33$
$\therefore \left(\frac{150}{300}\right)=\left(\frac{10}{V_{2}}\right)^{0.33}$
or $\left(\frac{1}{2}\right)=\left(\frac{10}{V_{2}}\right)^{0.33}$
or $\left(\frac{1}{2}\right)^{3}=\frac{10}{V_{2}}$
or $\frac{1}{8}=\frac{10}{V_{2}}$
or $V_{2}=80\, L$