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JEE Main levelSingle correct optionDifficulty 2 of 3td137

Two moles of an ideal gas expand reversibly and isothermally from $5.0 L$ to $20.0 L$ . With $R = 8.314 J mo l^{- 1} K^{- 1}$ , $Δ S_{sys}$ is closest to

A $11.5 J K^{- 1}$
B $10.0 J K^{- 1}$
C $66.5 J K^{- 1}$
D $23.1 J K^{- 1}$

Answer: D

For an isothermal ideal-gas expansion

Δ S = n R ln (V_{2} / V_{1}) = 2 \times 8.314 \times ln 4 = 23.1 J K^{- 1}

. Omitting

n

gives

11.5

, using

lo g_{10}

gives

10.0

and dropping the logarithm gives

66.5

.

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