Calculate the entropy change accompanying the following change of state
`5 mol` of `O_(2) (27^(@)C, 1 atm) rarr 5 mol of O_(2) (117^(@)C, 5 atm)`
`C_(P)` for `O_(2) = 5.95 cal deg^(-1) mol^(-1)`

Explanation

`DeltaS_(1) = (q_(rev))/(T) = (W_(rev))/(T) = (1)/(T) xx int_(V_(1))^(V_(2)) P dV`
`= (1)/(T) nRT int_(V_(1))^(V_(2)) (dV)/(V) =nR xx 2.303 "log" (V_(2))/(V_(1))`
`= 5 xx 1.987 xx 2.303 "log"(P_(1))/(P_(2))`
`= 5 xx 1.987 xx 2.303 "log"(1)/(5) =- 16.0 cal deg^(-1)`
`DeltaS_(2) =` for the change of temperature form `27^(@)C to 117^(@)C`
`DeltaS_(2) nC_(P)int_(T_(1))^(T_(2))(dT)/(T)`
`= 5 xx 6.95 xx 2.303 "log" (390)/(300)`
`= 5 xx 6.95 xx 2.303 xx 0.1139`
`= 9.12 cal deg^(-1)`
`DeltaS =- 16.0 + 9.12 =- 6.88 cal deg^(-1)`