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Question:

The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of 10 dm³ to a volume of 100 dm³ at 27°C is:

38.3 Jmol⁻¹K⁻¹

42.3 Jmol⁻¹K⁻¹

35.8 Jmol⁻¹K⁻¹

32.3 Jmol⁻¹K⁻¹

Solution:

ΔU=0 for an isothermal process so Q=−W
W=−nRTln(V₂/V₁)
W=−2×8.314×(27+273)ln(10)
W=−11486.21 J
So, ΔS=q/T
ΔS=11486.21/300
ΔS=38.3 Jmol⁻¹K⁻¹