Question

A piston-cylinder assembly contains air modeled as an ideal gas. The air undergoes a power cycle consisting of four processes in series:

• Process 1-2: Constant-temperature expansion at 600 K from p1 = 0.5 MPa to p2 = 0.4 MPa.

• Process 2-3: Polytropic expansion with n = 1.3 to p3 = 0.3 MPa.

• Process 3-4: Constant-pressure compression to ν4 = ν1.

• Process 4-1: Constant-volume heating.

a) Sketch the cycle on a p-ν diagram.

b) Calculate the work and heat transfer for each process, in kJ/kg

Answer 1

Pi-0.5 mPa . M P2-0.4 | .-- - mpa la 0.3ml L » Pin = RTI >>(0.5) V, = 287X 600 = 344400 ming in V2 = (2.25) V2 - : :. V2 = (0 ) va Pz 121.3) = Ps VGS 32.3 X I. 25 . V3 = ( Pz 7.3 Pax V2 = ( 1 V3 = 1.56 Yı → V4 = V2 * work done | W = RTz bnc) + Pava - Pava - P3 (VG-64) * 287 X 600 in (1.25) + 0.032x344400 -0.3(0.56) 1.4-1 C344400) W: 8118.12 J/kg Eneasy tomsked and work in each process : > 1-2:- Iso theomal! Wiza RTz tn CV2) = 287 x 600 in (1.25). Wiza 38425,32 J/kg QiZ = Wiz = 38425-32 g/kg

>> 2-3 :. puls3 - C 752= PzV2 - Ba Vg 0.4x1.25V - 0.3x)256V, K-I I.3-1 W22 - 0.032 X244400 3 - 0.3 < = 36736 J/k9 Oz w toffee (Parg = Pive) R Pz3 = 36736 + (-0.032 X 344400) Ou4 Pe3= 9784 J/kg >> 3-4 ; P=C = 0.3 mpa NBA- PB Cr2_V3 ) =-0.3 x0.56 x 344400 134 = -57859.2 J)/19 Op w E PAYA-P33 T-1 í 0.3 (-0.56% 344400) Q3x = -57859.2 + 0.4 Q34 -- 202507. 2 JlKg = 4-1 ;. I sochoaja NFO 172200 - 103320 -1 0.4. P41 = 172200 J/kg.