**Entropy**

First
I would define Entropy in the most succinct way “Energy depends to
disperse”. So everything from a candle being lit that disperses
heat energy out from the flame, to a rock being dropped into a pool
of water and the energy going out in the form of the ripples and
splashes.

Heat
energy dispersing then leads on to the heat death of the universe.
This is a suggested ultimate fate of the universe, in which all the
heat from all the stars and other processes will have dispersed all
there energy so that the universe is left in a thermal equilibrium.
If this were to happen then there would be no energy left to produce
work and so no more processes would be able to occur and the universe
would more or less than come to a stop. The name “Heat Death”
implies extraordinarily high temperatures however this is not the
case is all the heat energy were to disperse it would result in a
very low temperature due to the sheer size of the universe and the
finite amount of heat energy being spread over it.

I
would then say that there is more to entropy than that and that it
involves several different definitions of different processes
involved in thermodynamics, starting with the zeroth law of
thermodynamic. The zeroth law is a very simple and somewhat obvious
statement, it states “If two systems are in thermal equilibrium
with a third system, then they must be in thermal equilibrium with
each other”. In other words systems are in thermal equilibrium when
they all have equal temperatures.

From
this I would lead onto the first law of thermodynamics. The first law
is simply a statement of the conservation of energy “(Change in U)
= (Change in Q) + (Change in W)” where U is the internal energy, Q
is the heat energy and W is the work done. This is why the “Heat
Death” would occur as since there would be constant heat energy Q,
there can subsequently be no change in the Work done W. It is
important to note the Q and W are functions of state. This means that
they do not depend on the history of how they got to that state. So,
they can travel by any path and the path they took does not influence
the final value.

Now
the next most important system to consider is reversible and non
reversible processes. A reversible process is one that can be undone
without resulting in any change to the system or its surroundings,
now this is unfortunately not possible and is an idealized process as
for instance you cant un-bake a cake, or un-pop a balloon. But even
on a much smaller level, if you wheel your chair across a room a
breeze is created and when you wheel it back another breeze is
created. the previous breeze is not sucked back towards the chair.
However, in general the main thing that cannot be undone is the
entropy of the system because as we will find out. Because in nature,
entropy always increases.

Take
for instance the graph shown in figure 1 , if the process was
reversible then the area under the graph would be zero and so nothing
would change, However, since there are no reversible processes the
path back to the starting point will be not be equal to zero and so
will result in some amount of work done. But, if this happens the
change in internal energy will be zero as it has returned back to the
starting point so if you look at the first law of thermodynamics this
implies that the heat energy is equal to the negative of the work
done. In other words, heat in = work out, and work in = heat out.

Figure
1. Area under the graph of pressure against volume is the work done.
In more mathematical terms dW = -p dV where p is the pressure and dV
is the change in volume.

I
would then go on to talk about the Carnot cycle. The Carnot cycle is
a very important process that describes and idealised heat engine,
one which in reality is not achievable but is important in the
fundamental understanding of thermodynamics. It is best explain with
use of a diagram shown in figure 2.

Figure
2. Diagram of the Carnot cycle which runs from point A-B, B-C and so
on back to point A.

From
figure 2 it should be said that the green lines pointing up and down
are adiabatic processes which is a process that occurs without loss
or gain of heat, and the lines marked T1 and T2 are isothermal which
simply means they occur at constant temperatures. This is a process
that uses an ideal gas which again is not attainable in reality but
helps to define what is happening. So the gas is expanded from A-B
and B-C and then compressed from C-D and D-A taking it back to its
original point. Q1 is the heat into the system at a higher
temperature and Q2 is the heat going out of the system at a lower
temperature.

From
this the thermal efficiency can be calculated by dividing the work
out by the heat energy in and it is found that this must be less than
one due to Clausius's statement which we shall come back to later.
This shows that no system, apart from an idealized one, can be 100%
efficient. This is important to know apart from the implications in
to creating efficient engines and such in real life but it also
implies that no matter what you do energy will be lost. In a sense,
entropy is the measure of the amount of energy that is not available
to be converted to work in the system. E.g. how much energy is lost
and this, is the second law of thermodynamics.

I
would then go on to explain more details of the second law. The
second law of thermodynamics can be quite hard to define and
understand conceptually. There are two statements of the second law
of thermodynamics that are vital in our understanding of it. The
first is Clausius's statement which is “No process is possible
where the sole result is the transfer of heat from a colder to a
hotter body.”. The second is Kelvins statement which is “No
process is possible whose sole result is the complete conversion of
heat into work” and this relates back to what was defined with the
Carnot cycle.

These
two statements are of paramount importance even though they do seem
somewhat obvious it is important to consider that if they did not
explicitly define these facts then they would be up for
interpretation and could have changed the way many systems were
considered and not for the better.

Together
they can be used to disprove any other form of engine apart from the
one which we know and use today in which heat goes into the engine,
work is put out but there is also an exhaust to vent any excess heat.

Mathematically
entropy, S, can be defined as dS = dQrev/T where dS is the change in
entropy, dQrev is the change in heat energy in an reversible system,
and T is the temperature. This results in the unit of entropy being
J/K or Joules per Kelvin which makes sense when entropy is the
measure of energy lost of a system at a given temperature.

Finally
we must look at the fundamental equation of thermodynamics. First
remember the 1

^{st}law of thermodynamics: dU=dQ+dW, and we also now that dW = -pdV and finally we know that the entropy change of a reversible process is: dS = dQrev/T. If we put all these equations together we get the final equation:
dU=TdS-pdV in a reversible process.

But,
it should be noted that all these terms are functions of state and so
do not depend on the path they took which means that this equation
must also hold true for irreversible processes. This is the
fundamental or central equation of thermodynamics as it allows
entropy to be meausred as a physical value of all systems.

Although your approach is technically correct, I would try mixing in more daily life examples as well as some humour.

ReplyDeleteWhy do our rooms get messy? Why do we have to constantly clean up? Why do car engines create so much heat?

Why is it easy to mix salt and pepper but not easy to separate them?

Why do warm things cool and cool things warm to the ambient temperature around them? Why doesn't a cup of coffee get hot on its own? Why doesn't my soft drink Getty child on its own?

Etc. Hope this helps! Good luck!

Thanks very much for the reply! That seems to be a good Idea I'll try add in some more examples like that through out. Cheers!

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