$\pu{10 L}$ of a monoatomic ideal gas at $\pu{0 ^\circ C}$ and $\pu{10 atm}$ pressure is suddenly released to $\pu{1 atm}$ pressure and the gas expands adiabatically against this constant pressure. What are the final temperature and volume of the gas? (Answer: $\pu{174.9 K}$, $\pu{64.04 L}$)
There are some points I don't get:
- First of all, it is not given whether it is reversible of irreversible expansion.
- If it is reversible, I am at wits end deciding whether to use one of the following (without success): $$ pV^\gamma = \mathrm{constant} \quad \mathrm{or} \quad T^\gamma p^{1 - \gamma} = \mathrm{constant}$$
- If it is irreversible, I tried using
$$W_\mathrm{irreversible} = \Delta E$$
i.e. $$-P_{ext} \left(\frac{nrT_2}{p_2} - \frac{nrT_1}{p_1}\right) = nC_\mathrm{v}\Delta T$$ I am having trouble using $r = \pu{0.0821 L atm mol-1 K-1}$ and $R = \pu{8.314 J mol-1 K-1}$.