Question

When $1$ mole of $C{O}_{2(g)}$ occupying volume $10L$ at $27^{\circ }C$ is expanded under adiabatic condition, temperature falls to $150K$. Hence, final volume is

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

Answer 1

Answer: (D)

For adiabatic expansion
$\frac{T_2}{T_1}={\left(\frac{V_1}{V_2}\right)}^{\gamma -1}$
Here, for $C{O}_2$ (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 $V_2=80L$