Sonntag, Borgnakke and van Wylen
4.57 Find the work for Problem 3.106. Refrigerant-12 in a piston/cylinder arrangement is initially at 50°C, x = 1. It is then expanded in a process so that P = Cv−1 to a pressure of 100 kPa. Find the final temperature and specific volume. Solution: Knowing the process (P versus V) and states 1 and 2 allows calculation of W. State 1: 50°C, x=1 Table B.3.1: P1 = 1219.3 kPa, v1 = 0.01417 m3/kg Process:
v2 P = Cv-1 ⇒ 1w2 = ∫ P dv = C ln v 1
State 2: 100 kPa and on process curve:
same as Eq.4.5
v2 = v1P1/P2 = 0.1728 m3/kg
From table B.3.2 T = - 13.2°C The constant C for the work term is P1v1 so per unit mass we get v2 0.1728 w = P v ln 1 2 1 1 v = 1219.3 × 0.01417 × ln 0.01417 = 43.2 kJ/kg 1
T
P
1
1
2
2 v
Notice T is not constant. It is not an ideal gas in this range.
v