One mole of an ideal gas at $300 K$ doubles its volume, once by (I) a reversible isothermal expansion and once by (II) a free expansion into vacuum. Use $R = 8.314 J mo l^{- 1} K^{- 1}$ . Select the correct statement(s).

Answer: A, C, D

Δ S_{sys} = R ln 2 = 5.76 J K^{- 1}

for both, because

S

is a state function (statement 1 true). In (I) the gas absorbs heat

q_{re v} = RT ln 2

from the surroundings, so

Δ S_{s u rr} = - 5.76

and

Δ S_{u ni v} = 0

; statement 2 has the wrong sign. In (II)

q = 0

, so

Δ S_{s u rr} = 0

and

Δ S_{u ni v} = Δ S_{sys} = + 5.76

(statements 3 and 4 true).