Upload
captainhass
View
218
Download
0
Embed Size (px)
Citation preview
8/7/2019 10.thermo
1/5
MIT OpenCourseWarehttp://ocw.mit.edu
5.60 Thermodynamics & Kinetics
Spring 2008
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
http://ocw.mit.edu/http://ocw.mit.edu/http://ocw.mit.edu/termshttp://ocw.mit.edu/termshttp://ocw.mit.edu/8/7/2019 10.thermo
2/5
5.60 Spring 2008 Lecture #10 page 1
Entropy and Disorder
Mixing of ideal gases at constant Tand pnA A (g, VA, T) + nB A (g, VB, T) = n(A + B) (g, V, T)
nVA
nVB
nVB
spontaneous +n =nA B A Bmixing V V += A
To calculate Smix , we need to find a reversible path between
the two states.
constant T A B
A + B
piston piston back to initial statepermeable permeable
to A only to B only
Sdemix = Smix function of stateFor demixing process
U =0 q = w =pdV +pdVrev rev A A B Bwork of compression of each gas
S = dqrev = VA pAdVA + VB pBdVB =nRlnVA +n RlnVBdemix T V T V T A V B VPut in terms of mole fractions XA =nA XB =nBn n
Ideal gas XA =VA XB =VBV V
8/7/2019 10.thermo
3/5
5.60 Spring 2008 Lecture #10 page 2
Sdemix = nR XAlnXA XB ln B[ + X ] Smix = nR XAlnXA XB ln B [ + X ]
Since A, < 1 Smix > 0 mixing is always spontaneousX XB
The mixed state is more disordered or random than the
demixed state.Smixed > Sdemixed
This is a general result
Entropy is a measure of the disorder of a system
For an isolated system (or the universe)
>S 0 Spontaneous, increased randomness
=S 0 Reversible, no change in disorder
8/7/2019 10.thermo
4/5
5.60 Spring 2008 Lecture #10 page 3
(b) Heating (or cooling) at constant VA (T1, V) = A (T2, V)
S T2 C dT if CV is = qrev = T V = C lnT2T 1 T T-independent V T1[Note S > 0 if T2 >T1 ]
(c) Reversible phase change at constant Tand pe.g. H2O (l, 100C, 1 bar) = H2O (g, 100C, 1 bar)
qp = Hvap
vap ( ) qpvap = Hvap (Tb = boiling Temp at 1 bar)S 100 C =Tb Tb
(d) Irreversible phase change at constant Tand pe.g. H
2O (l, -10C, 1 bar) = H
2O (s, -10C, 1 bar)
This is spontaneous and irreversible. We need to find a reversible path between the two states
to calculate S.
irreversible
H2O (l, -10C, 1 bar) = H2O (s, -10C, 1 bar)qrev = Cp( )A dT qrev = Cp (s)dT
reversible
H2O (l, 0C, 1 bar) H2O (s, 0C, 1 bar)=revqp = Hfus
8/7/2019 10.thermo
5/5
5.60 Spring 2008 Lecture #10 page 4
S S + = Sheating + fus Scoolingfus p( )dT Hfus T1 Cp( )s dTT C A= T1 T + Tfus + Tfus T
= T
+ T1 C A C s T SHfus Tfus
p( ) p( ) dT
=Hfus C ( ) ( ) lnTfus if Cp values are T-independentS
T+ p A Cp s T1