2 14 marks total A cylinder A with a frictionless piston is

2. (14 marks total) A cylinder A with a frictionless piston is connected to a tank of volume V, 0.1 m. The tank is initially filled with air at T 60°C and P81 700 kPa, while the cylinder initially contains 0.01 m3 of air at T 20°C. The piston exerts a constant pressure of PAI200 kPa until it reaches the end of the cylinder, at which point the volume is VA- 0.02 m. The valve isA then opened, and air flows from B to A until a final uniform state is reached (P-P , TA-T) Cylinder A and tank B are insulated. (a) (8 marks) Assuming that the piston reaches the end of the cylinder, determine the work done in kJ and the final temperature. You may assume constant specific heat. (b) (4 marks) Prove that the piston reaches the end of the cylinder. (c) (1 mark) Explain in words why the temperature changes as it does. (d) (1 mark) Is this a quasi-equilibrium process? State why or why not.

Solution

Cont.: m₂= m₁ = m_A1 + m_B1

P_B1V_B1        = P_A1 (V_A1-V_A2)

P_B1 = 700 Kpa

V_B1   = 0.1 m3

T_B1 = 60 Deg C = 333 K

R=0.287

₌ 0.01 m3

       = (700* 0.1)/(0.287*333)

       = 0.732 kg

       = (200* 0.01)/(0.287*293)

       = 0.023 kg

m₂=m₁= m_B1+m_A1

= 0.755 kg

Final Pressure

   P_A2=P_A1= 200 KPa

V_A2=V_B2

Work Done = P_A2(V_A2-V_A1)

                = 200*(0.02-0.01)

                = 2 KJ

T_A2=P_A2 V_A2/m_tot*R

                = (200*0.02)/(0.755*0.287)

                = 18 K