Sonntag, Borgnakke and van Wylen
5.127 Consider the system shown in Fig. P5.127. Tank A has a volume of 100 L and contains saturated vapor R-134a at 30°C. When the valve is cracked open, R-134a flows slowly into cylinder B. The piston mass requires a pressure of 200 kPa in cylinder B to raise the piston. The process ends when the pressure in tank A has fallen to 200 kPa. During this process heat is exchanged with the surroundings such that the R-134a always remains at 30°C. Calculate the heat transfer for the process. Solution: C.V. The R-134a. This is a control mass. Continuity Eq.: m2 = m1 = m ; Energy Eq.5.11: Process in B:
m(u2 − u1) = 1Q2 - 1W2
If VB > 0 then
P = Pfloat (piston must move)
⇒ 1W2 = ∫ Pfloat dV = Pfloatm(v2 - v1) Work done in B against constant external force (equilibrium P in cyl. B) State 1: 30°C, x = 1. Table B.5.1: v1 = 0.02671 m3/kg, u1 = 394.48 kJ/kg m = V/v1 = 0.1 / 0.02671 = 3.744 kg State 2: 30°C, 200 kPa superheated vapor Table B.5.2 v2 = 0.11889 m3/kg, u2 = 403.1 kJ/kg From the process equation 1W2 = Pfloatm(v2 - v1) = 200×3.744×(0.11889 - 0.02671) = 69.02 kJ From the energy equation 1Q2 = m(u2 - u1) + 1W2 = 3.744 ×(403.1 - 394.48) + 69.02 = 101.3 kJ