Question

If \( 10 mol \) of an ideal gas expands reversibly and isothermally from \( 10 L \) to \( 100 L \) at \( 300 K \), then entropy change will be

(1) -191.47 \( J K ^{-1} mol ^{-1} \)

(2) \( 191.24 JK ^{-1} \)

(3) \( 83.03 J K ^{-1} \) 

(4) \( 83.03 JK ^{-1} mol ^{-1} \)

Answer 1

Correct option is (2) 191.24 J K^-1

As we know

\(\Delta S = nC_V\, ln\frac{T_2}{T_1} + nR\,ln\frac{V_2}{V_1}\)    .....(1)

∵ Expansion occurs, reversibly and isothermally.

∴ The above equation (1) becomes-

∴ \(\Delta S = nR\, ln \frac{V_2}{V_1}\)    .....(2)

Putting the values of n, R, V₂ and V₁ in equation (2) - 

\(\Delta S = 10\times 8.314 \times ln \frac{100}{10}\)

\(= 2.303 \times 10\times 8.314 \times log 10\)

\(= 191.47 JK^{-1}mol^{-1}\)