A heat engine having an ideal monatomic gas as a working substance has a cycle c

Question

A heat engine having an ideal monatomic gas as a working substance has a cycle consisting of the following three processes:
Isobaric expansion at 200 kPa with volume change from 0.100 m^3 to 0.230 m^3,
an isovolumetric process at 0.230 m3 with pressure change from 200 kPa to 50.0 kPa, and an adiabatic process. The temperature at the beginning of the isobaric process is 300 K.

(a) Draw the cycle on a P - V diagram. (not necessary)
(b) Find the temperatures at points A, B, and C.
(c) Find the internal energy at points A, B, and C.
(d) Find the work done by the engine for each process and the amount of heat
flowing into or out of the system for each process.
(e) Find the total work done by the engine and its efficiency.

I would really appreciate if someone could help me out!

Explanation / Answer

No. of moles of substance, n = PV/RT = 8.019 b) Ta = 300 K Tb = PV/nR = 690 K Tc = PV/nR = 172.5 K c) For monoatomic gas, Cv = 3R/2 Ua = nCvTa = 30000 J = 30 kJ Ub = nCvTb = 69 kJ Uc = nCvTc = 17.25 kJ d) Work = W1 + W2 + W3 = P dV + 0 + (nRT1 - nRT2)/(Y - 1) ; Y = gamma = Cp/Cv = 5/3 = 200000* 0.13 + (nR*-127.5)/(2/3) = 13.25 kJ {W1 = 26 kJ ; W2 = 0 ; W3 = 12.75 kJ} Q = -W = -13.25 kJ [Delta U = 0] e) Total work = 13.25 kJ

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