Three moles of an ideal gas `(C_(v,m) = 12.5 J K^(-1) mol^(-1))` are at `300 K` and `5 dm^(3)`. If the gas is heated to `320K` and the volume changed to `10 dm^(3)`, calculate the entropy change.

Explanation

The entropy changes as a funciton of `T` and `V` is
`DeltaS = nC_(V,m) "In"(T_(2))/(T_(1)) +nRT "In"(V_(2))/(V_(1))`
`DeltaS = (3 mol) xx (12.5 JK^(-1) mol^(-1)) xx 2.303`
`"log"(320)/(300) +(3mol) xx (8.324 J K^(-1)mol^(-1)) xx 2.303 "log"(10)/(5)`
`= 2.42 J K^(-1) + 17.29J K^(-1) = 19.71 JK^(-1)`