Introduction to Carbon Capture - Introduction to Carbon Capture and Sequestration - page 151

The entropy change is given by:

∆ S sep n cap s mix ( x cap ) n exh s mix ( x exh ) − n fl ue s mix ( x fl ue ), = +

where s mix is the molar entropy of the mixture with the given composition.
We will use the convention that the total entropy of the system is written
as S , while the entropy per mole is written as s . We will use a similar
convention for the energy ( U and u ) and work ( W and w ). The molar
entropy of mixing two components is given by:

mix

∆ s

( ) ( )

=− xx ln − 1 − x ln 1 − x ,

k

B

where x is the mole fraction of one of the components. This formula can
be derived from statistical thermodynamics (see Box 4.2.2 ).
Figure 4.2.1 suggests that we have 6 variables in the carbon capture
process. However, not all variables can be controlled independently. As
the total number of moles needs to be conserved, we have:

n fl ue = n exh + n cap ,

Box 4.2.2 Entropy of mixing

Boltzmann has shown that the entropy S is related to the total number of confi gura-
tions Ω accessible to a system:

S = k B ln Ω

To illustrate how we count the total number of confi gurations, consider a lattice model
with N A molecules of type A (red) and N B molecules of type B (blue). Each lattice site
is occupied by exactly one molecule. If the system is separated into two compart-
ments, there is exactly one way in which we can put the blue and red molecules on
the lattice ( Ω A = 1 and Ω B = 1). If we allow the system to mix, the total number of confi gu-
rations is given by:

( )

NN

N +

!

A B

Ω=

AB

! !

AB