Question

4) A gas contained within a piston-cylinder assembly undergoes four processes in series: Process 1-2. Expansion with Pr= constant, P,-3 bar, p, = 0.2 m, P2-2 bar, U-U-200 kJ. Process 2-3: Constant volume cooling of the gas to 1 bar, with Us 100 kJ. Process 4-1: Expansion with PV constant. a) Evaluate V2 and V4, each in m3 b) Sketch the processes in series on a P-V diagram labeled with pressures and volumes at each numbered state c) Evaluate the work and heat transfer for each process, in kJ. For each process, state the direction of energy transfer by work and heat (into or out of the system). d) Determine the net work and the net heat transfer during all four processes

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Answer 1

(c_p) gas = 0.718 ks process 1-2 PV = constant P_1 = 3 bar: V_1 = 0.2 m^3: P_2 = 2 bar V_2 = P_1 V_1/P_2 = 3 times 0.2/2 = 0.3 m^3 U_1 = U_2 = 200 K J = C_v T: T_1 = T_2 = 200/0.718 = 278.55 K dw = P_1 V_1 ln V_2/V_1 = 3 times 10^2 times 0.2 ln 0.3/0.2 = 24.327 K J d theta - dw = du d theta = dw = 24.327 K J process 2-3: V = C: T_3 = 100/0.718 = 139.275 K P_3 = 1 bar: U_3 = 100 K J: V_3 = 0.3 m^3 dU = U_3 - U_2 = 200 - 100 = 100 K J d theta - dw = dU d theta - 0 = 100 K J d theta = 100 K J: dw = 0: dU = 100 K J process 3-4 P = C