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.

The molar heat capacity at constant pressure of O_(2) is given by bar

1.	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.
Answer» Solution :`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)`