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JEE Main levelSingle correct optionDifficulty 2 of 3td044

One mole of ideal gas A and three moles of ideal gas B, both at the same temperature and pressure, are mixed at constant $T$ and $P$ . With $R = 8.314 J mo l^{- 1} K^{- 1}$ , the entropy of mixing is

A $- 18.70 J K^{- 1}$
B $23.05 J K^{- 1}$
C $+ 18.70 J K^{- 1}$
D $11.53 J K^{- 1}$

Answer: C

Δ_{mi x} S = - R \sum n_{i} ln x_{i} = R [1 ln 4 + 3 ln (4/3)] = 8.314 (1.3863 + 0.8630) = 18.70 J K^{- 1}

. It is positive because each gas occupies a larger volume after mixing.

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