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ds = RlnP2/P1, ds > 0
q2: what is ds for system undergoing adiabatic irr. process
ds = sint(Q/T) + sigma, adiabatic ;; ds > 0
q3: reversible adiabatic process
- reversible = quasi-equilibrium
- isotropic ds >0
- sigma = 0
q6: T1 to T2 change in entropy fast v slow?
-state variable, state function
-entropy production -- process, path function, does matter
-----------------------------
Isentropic Efficiencies
ideal --> isentropic, adiabatic, reversible
Nozzle: V2>V1, P2<P1
Assume: s.s, PE=0,
dE/dt = Q.- W. + m.(h1+V1^2/2)-m.(h2+V2^2/2) --- W.=0
V2^2 = 2[(h1-h2)+Q./m.]+V1^2 ---ideal where Q.=0
V2^2 = 2[(h1-h2)]+v1^2
non-ideal --> Q. exists OUT
Nnozzle = V2s^2/2/V2^2/2 (compares KE & not velocity)
Turbine
s.s., neglect KE & PE
dE/dt = Q. - W. m.(h1) - m.(h2)
W.s/m. = h1 -h2s (ideal turbine)
For irreversiblities: (W./m.)act = (W./m/)ideal - (work lost to entropy)
(h1-h2)act < (h1-h2s)ideal
Nturbine = W.t/m./(W.t/m.)s = h1-h2/(h1-h2s)
***h2s = isentropic state
Compressor (s.s., KE = PE = 0)
dE/dt = Q. -W. +m.(h1-h2)
ideal, Q. = 0:
W./m. = h1 -h2s; W.<0
flip neg. sign
W./m. = h2s-h1 (same thing)
Ncomp/pump = h1-h2s/h2s-h1
------------------
Ex1:
1st law: dE/dt = Q. ;; Q.1=Q.2
2nd law: dS/dt= sum(Q/T) + sig.; sig. = -sum(Q./T) = -(Q.1/T1+Q.2/T2)
(Q.1/T1+Q.2/T2) < 0; Q.2/T1 < Q.2/T2; Q.1/Q.2 < T1/T2 ;; T1/T2 > 1 ;; T1>T2
--------------
Ex2: water vapor 5 bar, T1=320C, AV=0.65m^2/s to 1 bar T2=160C (adiabatic expansion)
a) power dev.
b) sig.
c)Nturbine
a) dE/dt = -W. +m.(h1)-m.(h2)
W. = m.(h1-h2); T & P at both states set, m. = AV/m
b) dS/dt = sum(Q./T) + m.s1-m.s2 + sig. (s.s, dS/dt=0, adiabatic)
sig. = m.(s2-s1)
c) superheated vapor
h1= 7.532
s1 = 3105.9
s2 = 7.661
h2s = 2791.4 (interpolate)
---------------
Ex3: incompr. at m1, c1, Th, through cycle comm. w/ m1, c1, Tc, cycle prod. W. until thermal eq. reached. what is Wmax?
dU = W = mc(Tf-Th) + mc(Tf-Tc)
W = mc[Th + Tc -2Tf]
2nd law: ds = sum(Q/T) +sig ; sum(Q/T) = 0
sig = ds = dshot + dscold
for incompressible
subs d(dens) = 0, ds= clnT2/T1
sig = mclnTf/Th + mclnTf/Tc = mclnTf^2/ThTc
Tf = sqrt(ThTc)
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