`1 mol` of an ideal gas is allowed to expand isothermally at `27^(@)C` untill its volume is tripled. Calculated `Delya_(sys)S` and `Delta_(univ)S` under the following conditions:
a. The expansion is carried out reversibly.
b. The expansion is a free expansion.

Answer

(a). `DeltaS_(sys)=9.135JK^(-1)mol^(-1)`
`DeltaS_(surr)=-9.135JK^(-1)Mol^(-1)`
`DeltaS_(univ)=0`
(b). `DeltaS_(univ)=DeltaS_(sys)=9.135JK^(-1)mol^(-1)`

Explanation

(a) In isothermal reversible process:
`DeltaS=(q_(rev))/(T)`
`q=-W=2.303nRT" log "(V_(2))/(V_(1))`
`=2.303xx8.314xx300lo3=2730.6J" "mol^(-1)`
`DeltaS_("system")=(q_(rev))/(T)=(2740.6)/(300)=9.135JK^(-1)mol^(-1)`
`DeltaS_(univ)=0`
(b) IN case of free expansion
`DeltaS=2.303nR" log "((V_(2))/(V_(1)))=9.135JK^(-1)mol^(-1)`
`DeltaS_(univ)=DeltaS_(sys)=9.135JK^(-1)mol^(-1)`
`DeltaS_(surr)=0`.