Question

A cylinder fitted with a frictionless piston contains stops arranged as shown in the following figure. When the piston rests on the lower stops the volume is 0.4m3 ; when it is in contact with the upper stops the volume is 0.6m3 . If the piston is not in contact with the stops, it maintains a constant pressure of 200kPa in the cylinder. Initially, the cylinder contains air at P1=150kPa with a temperature of T1=300K. The air is then heated until it reaches a temperature of T2=700K. Assuming constant specific heats (evaluated at 500K) throughout the process:

a) Does the piston contact the upper stops in the final state? Determine the final pressure. (7 marks)

b) Show the process on a P-v diagram. (3 marks)

c) Calculate the work done during the process. (2 marks)

d) Calculate the heat transfer during the process. (6 marks)

Air

Answer 1

1 Pi = 150 kPa, T, = 300K, V, -0.4m3, Pe- ?, Tę = 700k. Let, the piston does not touch the upper stops, then P2=2ookPa 1 P.VI. Pele 700 x 0.4 = 0.7m3 300 1 OUY a Pivi. Ne> 0.6m3 or assumption is wrong The piston contact the upper stop: - Ve= 0.6m3 Pq VL Ti Tz (4) 700 | X 150 kPa Pee 233.33 kPa Pez )x Pia Jx 300 P 233.33%! Look Pa Jokp

Work dones. W: -P(Ve- v.) =-200kPa (0.6-0.4)m3 W = -40kJ AU = 0 tw (Ist law of thermodynamic's). ♡ - AU-W En Cu(T₂-T,Jow for air ) Cu= 21.4 J/mol-ke. n=pivi 150 x 103 x 0.4 RT, 24.056 P-314 X300 24.057 X 21-45/al.k ( 700-300) -(-40X 109) Q=245.92 kJ Heat transttered.