Question

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

• A. $5 \,L$
• B. $20 \,L$
• C. $40\, L$
• D. $80\, L$

Answer 1

Answer: (D)

$80\, L$

Answer 2

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 $V_{2}=80\, L$