A sample of an ideal gas is expanded to twice its original volume of `1m^(3)` in a reversible process for which `P = alphaV^(2)`, where `alpha = 5 atm m^(-6)`. If `C_(V,m) = 20 J mol^(-1)K^(-1)`, determine moalr change in entropy `(DeltaS_(m))` for the process.

Explanation

Using
`DeltaS = nC_(V) In (T_(2))/(T_(1)) + nR In (V_(2))/(V_(1)) (n = 1)`
and `(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))`
`rArr (T_(2))/(T_(1)) = (P_(2))/(P_(1)).(V_(2))/(V_(1)) = (V_(2)^(3))/(V_(1)^(3)) ( :' P = alpha V^(2)) = 8 ( :' V_(2) = 2V_(1))`
`rArr DeltaS =1 xx 20 xx In 8 + 8.134 In 2 = 45.8 J mol^(-1) K^(-1)`