Question

Hydrogen in a piston-cylinder is undergoing a polytropic compression from 1 atm and 20oC to 10 atm. The polytropic index n was experimentally-determined to be 1.22 for this compression process. Treat hydrogen as an ideal gas and assume the compression process is quasi-equilibrium. Answer the following questions: (a) Determine the temperature at the final state. (b) Determine the boundary work per unit mass. (c) Determine the heat transfer per unit mass. (d) Determine the specific volume at the final state.

Answer 1

the as ideal gas. so PVM = constant solution: - considering Polytropic process Here n = 1.22 I for th = 1.4 P = 1 ahm, P2 = 10 oth Ti = 20°c = 293 k n som I Here I R = 8.314 I x 1 km Petrovate = 2 2 2 = &R a z knie walka R = 4124.2 J prn=const. PV = MRT so v= met them a) plana" = comod. (E)=const. 1-1.22 * (13*= * = () - ** = ló) 7.22 TE = 443.8081 (b) work (W) = Pili-kale = MR (T-E) (n-1 (n-1) {w} = R(TC) = (4124.2) (293– 443.80) (1.22-1) work fefe unit moss (W) = -28.26175 (0) Heat (9= (ran)(w) = (+4=1:22 ) (-28-26 mg) 19=-12.717 mf (d) at final state & P = R Tz =14124-2) (443.80) = 1.80 mm (Ipx10135 7 -1 7-1 1.4-1

Port (oo decivation of heat transfoe in Polytropic process - we know - du = ctco -ctw we u already know aw = Vrlz 2 for adiabati (8-1) but for Polytropic - ctwa Ping-P V2 = MR (Ti-E2 ing (n-1 7-12 1. © Putting values: - MR (E-Tī ) +nR (Ti-To) 17-12T M-19 = cto @ MRCG- ** **] = -(1-r) Cirmy Cm] - orgo 2) MR (Ti-T) En-r) - co (-)(n-1); -) I So et ges-1 so to = (nor (dwl (Y-