final pressure 1 atm work done 2 J An ideal monatomic gas initially has a temper

Question

final pressure 1 atm work done 2 J An ideal monatomic gas initially has a temperature of 330 K and apressure of 5.60 atm. It is to expandfrom volume 400 cm3 tovolume 1300 cm3. (a) If the expansion is isothermal, what arethe final pressure and the work done by the gas? final pressure 1 atm work done 2 J (b) If, instead, the pressure is adiabatic, what are the finalpressure and the work done by the gas? final pressure 3 atm work done 4 J

Explanation / Answer

P2 = P1*(V1/V2) = 5.6 atm*(400 cm3/ 1300 cm3) = 1.72307692 ~ 1.72atm b) W = integral [P*dV] = nRT *integral [ dV/V] = nRT*ln(Vf/Vi) n = P1*V1/ (R*T) =>   nRT = P1*V1 Work = P1*V1*ln(V2/V1) = (5.6 atm*400cm3)*ln(1300 cm3/400cm3) *(101325 Pa/1atm)*(1m/100cm)3 W = 267 Joules b) P1*V1 = constant = P*V = 5/3 for monatomic ideal gas Pfinal = P1*(V1/Vf) = 5.60 atm*(400/1300)5/3 = 0.785 atm W = integral [ P*dV] = constant *integral[dV/V] W = constant/(-1) *[-1/V-1] = -constant/(5/3 - 1) *[1/Vf-1 -1/Vi-1] W = (-3*constant/2)*[1/[1300 cm3]2/3 - 1/[400cm3]2/3] constant = P1*V1 = (5.60 atm)*(400cm3)5/3 = 121605.909 atm*cm5 W = [-3*121605.909 atm*cm5 / 2]*[-0.0100248276cm-2] W = 1828.61741 atm*cm3 W= 1828.61741 atm*cm3 *(101325 Pa/1atm)*(1m/100 cm)3 W = 185 Joules

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