A gas within a piston–cylinder assembly undergoes a thermodynamic cycle consisting of three processes in series, beginning at state 1 where m = 0.40 kg, p1 = 1 bar, V1 = 1.5 m3, as follows: Process 1–2: Compression with pV = constant, W12 = -102 kJ, u1 = 424 kJ/kg, u2 = 780 kJ/kg. Process 2–3: W23 = 0, Q23 = -150 kJ. Process 3–1: W31 = 48 kJ. There are no changes in kinetic or potential energy. Determine Q12 and Q31, each in kJ.

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit