8.3 moles at 10 6 N/m 2 of an ideal gas( = 1.5) expands isobarically, during whi

Question

8.3 moles at 106 N/m2 of an ideal gas( = 1.5) expands isobarically, during which , it's volumeincreases by .083 m3 and its temperature increases by1200o C. a. How much work was done by the system? b) Howmuch heat was added to the system? c) what is the change ininternal energy of the system? How are these answers derived? Answers: a) 83 kJ b) 249 kJ c) 166 kJ 8.3 moles at 106 N/m2 of an ideal gas( = 1.5) expands isobarically, during which , it's volumeincreases by .083 m3 and its temperature increases by1200o C. a. How much work was done by the system? b) Howmuch heat was added to the system? c) what is the change ininternal energy of the system? How are these answers derived? Answers: a) 83 kJ b) 249 kJ c) 166 kJ

Explanation / Answer

a) W = integral [P*dV] = P*integral[dV] = P*V = (1e6N/m2)*(0.083 m3) = 83000 J = 83 kJ b) Q = moles*Cp*T = Cp = heat capacity =*Cv             Cv is heat capacity at constant volume Cp - Cv = R, a property of ideal gases Cp = *(Cp - R) Cp = R/ ( - 1) = R*1.5 / (1.5 - 1) = 3R Q = 8.3 moles*(3*8.314 J/mol/K) *(1200 K) = 248422.32 J = 249kJ c) U = Q - W = 249 - 83 = 165.43726 kJ ~ 166 kJ

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