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The molar heat capacity at constant pres...

The molar heat capacity at constant pressure of `O_(2)` is given by
`bar(C_(P)) = 25.723 + 12.979 xx 10^(-3) T xx 10^(-3) T - 38.618 xx 10^(-7) T^(2)`
If the temperature of the system containing 2 mol of `O_(2)` is heated from `27^(@)` C to `227^(@)` C and explained from `2dm^(3)` to `8dm^(3)`, calculate the change in entropy. Assume gas is ideal and the process is carried reversibly.

Text Solution

Verified by Experts

`DeltaS = nint_(T_(1))^(T_(2)) barC_(P).(dT)/P -nRln P_(2)/P_(1)`
`Deltas = 2mol int_(T_(1))^(T_(2))(25.723 + 12.979 xx 10^(-3) T - 38.618 xx 10^(-7) T^(2))(dT)/T + 2(8.314 J "mol"^(-1) K^(-1)) ln (8dm^(3))/(2dm^(3))`
`DeltaS = 2mol xx 25.723 JK^(-1) "mol"^(-1) int_(300)^(500) (dT)/T + 2mol (12.729 xx 10^(-3)) JK^(-2) mol^(-1) int_(300)^(500) dT + 2 mol (-38.618 xx 10^(-7)) JK^(-3) mol^(-1) int_(300)^(500) T propto T + 2 "mol" (8.314 J mol^(-1)K^(-1))ln 4`
`=53.28 JK^(-1)`
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