One mole of a monatomic ideal gas at $310 K$ and $10 bar$ expands adiabatically against a constant external pressure of $1 bar$ until it reaches mechanical equilibrium (take $R = 8.314 J mo l^{- 1} K^{- 1}$ ). Select all correct statements.

AThe final temperature is about $198 K$
BThe work done by the gas is about $1.39 kJ$
CThe final temperature is lower than it would be for a reversible adiabatic expansion to $1 bar$
DThe entropy change of the gas is zero because the process is adiabatic

Answer: A, B

Energy balance:

1.5 R (T_{2} - T_{1}) = - P_{e x t} (V_{2} - V_{1}) = - R (T_{2} - 0.1 T_{1})

, giving

T_{2} = 0.64 T_{1} = 198.4 K

and

w_{b y} = 1.5 R (T_{1} - T_{2}) = 1392 J

. The reversible adiabatic route to the same pressure gives

T = 310 \times 0. 1^{0.4} = 123.4 K

, which is lower, so the third statement is false.

Δ S = C_{P} ln (T_{2} / T_{1}) + R ln 10 = 9.87 J K^{- 1} > 0

for this irreversible process, so the last statement is false.