Question

$10L$ of a monoatomic ideal gas at $0^{o}C$ and $5atm$ is suddenly released to $1atm$ pressure and the gas is expanded adiabatically against the constant pressure. Find the final volume $\left(inL\right)$ of the gas.

• A. $54L$
• B. $10L$
• C. $34L$
• D. $74L$

Answer 1

The correct option is C $34L$

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