Question

$10\text{L}$ of a monoatomic ideal gas at $0{}^o\text{C}$ and $10\text{atm}$ is suddenly released to $1\text{atm}$ pressure and the gas is expanded adiabatically against the constant pressure. Find the final volume $\text{(L)}$ of the gas.

• A. $54\text{L}$
• B. $64\text{L}$
• C. $10\text{L}$
• D. $61\text{L}$

Answer 1

The correct option is B $64\text{L}$

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

For a monoatomic gas, $\gamma =1.67$

$\Rightarrow -1(V_2-10)$ = $\frac{1\times V_2-10\times 10}{\gamma -1}$
$\Rightarrow 10-V_2$ = $\frac{V_2-100}{0.67}$
$\Rightarrow (10-V_2)\times 0.67=(V_2-100)$
$\Rightarrow V_2=63.89\text{L}=64\text{L}$