Cambridge A level
H432 from 2015
Entropy
.
(a) explanation that entropy is a
measure of the dispersal of energy in a system which is greater, the more
disordered a system.
What is entropy?
As
you can see from this learning objective the definition of entropy is about
both the disorder of the particles of a system and the distribution of the
energy quanta in that system.
Let’s
use an argument from probability to illustrate the way in which energy quanta
are distributed among the particles in any given substance.
The
first assumption that we can make is this: if energy quanta are available to
share between molecules they will be shared in every way possible between all
the available molecules.
There
is assumed to be no restriction on the way in which the energy quanta are
shared.
So
if there are three molecules with three energy quanta to share between them
then they will share their quanta a total of 10 ways:
Number
of quanta
|
||
Molecule
1
|
Molecule 2
|
Molecule
3
|
3
|
0
|
0
|
2
|
1
|
0
|
1
|
1
|
1
|
2
|
0
|
1
|
1
|
0
|
2
|
0
|
3
|
0
|
0
|
0
|
3
|
0
|
1
|
2
|
1
|
2
|
0
|
0
|
2
|
1
|
Here
is the formula for calculating the number of ways of arranging quanta on a
given number of molecules.
Where
q is the number of energy quanta and m is the number of molecules over which
the quanta are shared.
The
example above is very simple and hardly representative of true states of
molecules and quanta because the real numbers are huge!
A
mole of molecules contains 6.02 ×1023 molecules and the quanta they
may possess may well be of a similar number.
To
give you an idea of the size of these numbers consider this situation: (you can
try and calculate these values to check for yourself if you want to!!)
Number
of molecules (m)
|
Number
of quanta (q)
|
W
the number of ways the quanta are shared.
|
100
|
10
|
1013
|
100
|
100
|
8×1059
|
200
|
110
|
1086
|
The
point of this exercise in statistical probabilities is this: the chances of all the quanta being arranged
in a particularly organised way of say one quanta per atom is highly unlikely.
As
we can see from the table above the chances of 100 quanta being arranged over
100 atoms with one quantum per atom is 1 in 8×1059
That
situation is very unlikely to occur.
From
this statistical model we conclude that changes that happen by chance tend to
go in the direction that will increase the number of ways of distributing the
molecules and energy quanta.
The
entropy of a system is related to W the number of ways in which the energy of a
system is dispersed over its molecules.
S =
k ln W
Where
S is the entropy of a system, ln W is natural logarithm of the number of ways
of arranging the energy quanta in the system and k is a constant called
Boltzmann’s constant.
So
from the Boltzmann formula we can see that if W increases so will S the entropy
of a system.
This
means that chemical change happens in the direction of an increase in W and S an increase in the total entropy of the system
For
a reaction to be feasible the total
change of entropy of both the system and surrounding has to be positive.
ΔStotal = ΔSsystem + ΔSsurroundings has to
be positive
Now
it ought from this to be clear that entropy increases with temperature since
any given substance has a greater number of quanta at a higher temperature.
As
a substance changes from solid to liquid to gaseous state its molar entropy
value will increase.
Note
that there is jump in entropy values when the substance changes state and melts
or boils.
All
this suggest that there is a temperature at which the entropies of all
substances is 0 and that that temperature is 0 Kelvins or absolute zero or
—273K.
At
this temperature all molecular motion has ceased completely.
All
substances have no energy quanta to disperse over their molecules.
And
as you can probably guess this situation is never realised in practice anywhere
in the Universe.
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