`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.

Explanation

a. In isothermla reversible process:
`DeltaS = (q_(rev))/(T)`
`q =- w = 2.303 RT "log" (V_(2))/(V_(1))`
`= 2.303 xx 8.314 xx 300 log 3 = 2740.6 J mol^(-1)`
`Delta_(sys)S = (q_(rev))/(T) = (2740.6)/(300) = 9.135 J K^(-1)mol^(-1)`
`Delta_(surr)S =- Delta_(sys)S =- 9.135 J K^(-1) mol^(-1)`
`Delta_(univ) S = 0`
b. In case of free expansion:
`DeltaS = 2.303 nR log ((V_(2))/(V_(1))) = 9.135 J K^(-1) mol^(-1)`
`Delta_(univ)S = Delta_(sys)S = 9.135 J K^(-1) mol^(-1)`
`Delta_(surr)S = 0`