One mole of an ideal gas at $300 K$ and $10 atm$ expands isothermally against a constant external pressure of $1 atm$ until its pressure is $1 atm$ , in contact with a large reservoir at $300 K$ . With $R = 8.314 J mo l^{- 1} K^{- 1}$ , $Δ S_{u ni v erse}$ is

Answer: D

Δ S_{sys} = R ln (P_{1} / P_{2}) = R ln 10 = 19.14 J K^{- 1}

. Heat absorbed

q = - w = P_{e x t} Δ V = 0.9 RT

, which the reservoir loses:

Δ S_{s u rr} = - q / T = - 0.9 R = - 7.48

. Sum:

Δ S_{u ni v} = 11.66 J K^{- 1} > 0

, as expected for an irreversible process.