Question

$10\text{L}$ of a monoatomic ideal gas at $O{}^{\circ }\text{C}$ and $5\text{atm}$ is suddenly released to $1\text{atm}$ pressure and the gas is expanded adiabatically against the constant pressure. Find the final volume $\left(\text{in L}\right)$ of the gas:

• A. $54\text{L}$
• B. $10\text{L}$
• C. $34\text{L}$
• D. $74\text{L}$

Answer 1

The correct option is C $34\text{L}$

For an adiabatic process $q=0$
From the First law, $\Delta U=q+w$
For an adiabatic irreversible process, $w=-P_{ext}(V_2-V_1)$
$w=\Delta U=\frac{P_2{V}_2-P_1{V}_1}{\gamma -1}$
$-P_{ext}(V_2-V_1)=\frac{P_2{V}_2-P_1{V}_1}{\gamma -1}$

For a monoatomic gas, $\gamma =1.67$
putting all the values,
$\Rightarrow -1(V_2-10)=\frac{1\times V_2-5\times 10}{\gamma -1}$
$\Rightarrow 10-V_2=\frac{V_2-50}{0.67}$
$\Rightarrow (10-V_2)\times 0.67=(V_2-50)$
$\Rightarrow V_2=34\text{L}$