I
ELDON L. KNUTH Department of Engineering, University of California, Los Angeles 24, Calif.
Isentropic Processes Involving Wet Vapors Processes which may be treated as reversible adiabatic processes involving wet vapors are encountered sometimes in the operation of engines, compressors, nozzles, pumps, and the like. Prospects of extracting power from a wetvapor stream using a turbine and a condenser were responsible for this work.
Dividing by T and rearranging, dT C,IY
+d
xAh ( 7= ) 0
This equation relates the change in vapor quality with the change in temperature or, alternatively, pressure for the isentropic conversion of the enthalpy of a wet vapor into pdu work effects. Consider now the important case in which the specific heat cal may be considered to have a constant value. Then the afore-mentioned equation may be integrated between definite limits to obtain
I N an isentropic process involving no work effects except those effects due to pdv work, the enthalpy and pressure changes are related by dh = v d p
with
h = specific enthalpy u = specific volume p = pressure
Subscripts 1 and 2 refer to the initial and final states, respectively, of the working substance. The only relatively minor limitation on the generality of this equation is that cS1is a constant.
For a wet vapor: Effects of p d v work and changes in internal energy are related by
h = hi $. xAh v = $- XAV
with x = weight fraction of substance in the vapor phase. The subscript 1 refers to the liquid phase, whereas the symbol A refers to the change in the thermodynamic property associated with the transition from liquid to vapor. Applying the first principle of thermodynamics to the liquid phase, one may write dhl = c,idT
with u u
specific internal energy = ui XAU =
+
Au--TT-
c , ~dT
688
dT
+ d(xAh) = (xAh) T
=
velocity
Substituting for xa, one obtains
This equation relates changes in velocity with the initial state and with the final temperature or, alternatively, final pressure. If the temperature difference is smalli.e., if Ti - Tz
