Vincent J. Curtis
9 July 23
The First Law of Thermodynamics equates the
system’s total internal energy E to the difference between heat, Q, and work, W. In differential form the equation is:
dE
= dQ – dW
You will notice the strike-throughs of the
differential notations before the Q and W terms. This indicates that these differentials are
inexact; and the reason they’re inexact is that in the course of adding heat to
the system some work can be done; and similarly some work being done by the
system can be converted into heat.
We see an example of this when we heat a
beaker of water on a hotplate. As heat
is added to the water at the bottom of the beaker, the water begins to move
around and circulate. This is work being
done. Similarly, when a solid is heated,
it is subject to thermal expansion; and this expansion is work. Some of the heat added to the solid was
converted into the work of expansion.
That’s why the heat capacity of a solid or liquid at constant pressure,
Cp , is different from the heat capacity at constant volume, Cv;
the heat capacity at constant pressure takes into account the energy required
to do the work of expansion. Just as in
expansion, when a solid cools, it will be subject to thermal contraction, and
this is negative work being done.
When the sun heats the earth, some of that
heat energy gets converted into work in the atmosphere. Air circulation patterns, wind, and weather
in general is work being done by the atmosphere as it is alternately heated and
cooled.
Climate change is supposed to result in
more intense storms. Since a storm is
work being done by the atmosphere, a more intense storm is one in which more work
is being done. Where is the energy to do
this extra work to come from? If E is
constant, the only place is from Q.
Somehow, the atmosphere, as a result of climate change, is supposed to
take more Q and convert it into more W.
The Second Law of thermodynamics says this is impossible.
The sun’s irradiation of the earth is
constant, meaning the sun isn’t providing more energy to drive the earth’s
weather systems. That means that E is a
constant. More W requires less Q. The Second Law of thermodynamics is:
dS
-dQ/T
where S is entropy, Q is heat and T is
absolute temperature. The negative sign
before the Q term is to account for the convention that heat is expressed as a
negative number. Entropy never
spontaneous becomes smaller. We never
see a beaker of water spontaneously separating into hot and cold regions. If the atmosphere spontaneously converted even
more heat Q into work W at constant E, that would result in a smaller Q, meaning
that S would become smaller; but this violates the Second Law. Hence, climate change that allegedly produces
more intense storms, or in general more work in the atmosphere, is impossible
because it requires the Second Law of Thermodynamics to be violated.
Note, insulation doesn’t solve the problem
for climate changers. Insulating the
solid that is being heated doesn’t change the amount of work done by thermal
expansion, or make the solid expand more at the same T. There is only so much internal energy
available to drive the earth’s atmosphere, and to put more energy into the
atmosphere so that it can do more work requires that heat to be taken from
somewhere else. But where?
The oceans are one place the atmosphere can
gain additional energy, and El Nino is one such phenomenon. Consistent with the First Law, the ocean
releases heat into the atmosphere and cools itself.
If the sun isn’t putting more energy into the
earth, where else can additional energy come from?
Energy in the earth’s atmosphere is
reflected to a great extent by temperature.
If the global atmospheric temperature were higher, would that mean more
heat in the atmosphere available to do work?
No, it wouldn’t, for at a constant E (regardless of what E is) the
conversion problem remains; the conversion of heat into work spontaneously has
an entropy problem. If E is constant, it
doesn’t matter at what T the conversion takes place.
The problem is resolved by recognizing that
it is during the process of heating and cooling that the doing of work
spontaneously is possible. Hence if the
sun were to heat the earth more intensely, then the spontaneous conversion of more
E into W is possible without an entropy problem. If Q remains constant, and all the additional
energy E is converted to W, the system doesn’t have an entropy problem because
S is not required to spontaneously get smaller.
Hence, it is only when the earth is being heated more intensely by the
sun, putting in more energy, that weather patterns can produce more W. If the sun were to decrease the energy it transferred
to the earth, making E smaller, during the transition not only would the
atmosphere cool, reflecting less Q, but work (technically, negative work) would
be done. (Just as a solid shrinks in
size due to thermal contraction. This is
negative work.) At a new level of solar
irradiation, a new system would be established.
This analysis is T independent, meaning that
the analysis holds regardless of what the underlying global average temperature
is. Whether the GAT is 287K or 291K, it
is the input of energy from sources external to the atmosphere that causes
weather, that is the doing of work W, in the atmosphere. And somehow, climate change is supposed to
alter the conversion ratio of input E into Q and W, emphasizing more W and less
Q. How tiny changes in atmospheric
composition is supposed to effect this remains a mystery.
Global warming, within reasonable limits,
does not impact the intensity of weather, or enable more work to the done by
the atmosphere.
-30-