Entropy and Information Theory

This post is part of a series,Nonsense and the Second Law of Thermodynamics The previous post is entitled  Partition Functions.

The posts in this series are primarily about the second law of thermodynamics, the concept of entropy, and the use and abuse of these ideas.  I would be remiss, however, not to mention information theory and the role that entropy plays.  This post is not intended to be a comprehensive introduction to information theory.  Readers especially  interested in this topic will want to read other sources in addition to this post.

Temperature Anomalies and Graphing Data

Globally Averaged Temperature Anomaly

One statistic that is used to understand climate is the annual globally averaged temperature anomaly.  It is not the only measure of global warming; there are a great many others, but it is one that the media tend to focus on because it is a convenient way of explaining what is happening to surface temperatures as a function of time.

The data here are taken from Global Land-Ocean Temperature Index (C) (Anomaly with Base: 1951-1980), which includes data from 1882-2007.  There are updated numbers available for more recent years, but I am using these data to respond to an argument made by a friend.

Partition Functions

This post is part of a series,Nonsense and the Second Law of Thermodynamics. The previous post is entitled Fluctuations.

In previous posts it was shown that entropy is related to the the number of ways that a system can arrange itself subject to constraints such as constant energy.

The previous post on fluctuations showed that for very large numbers that fluctuation from the most probable distribution, are insignificant.  Most of the distribution is contained within the square root of N of the most probable result.

Carbon Dioxide Poll

A recently closed poll on this blog posed the following question.  "The bending mode of carbon dioxide is:" Respondents were to respond with the best answer.  Here were the choices:

• A Hoax
• Not Dipole Allowed
• Degenerate
• A Blackbody
• The reason the sky is blue
• Even though I understand Global Warming, I don't know
• I don't know

I should point out that the answer to the question can be found in a post on this blog. The results of the poll are shown here:

Fluctuations

This post is part of a series,Nonsense and the Second Law of Thermodynamics The previous post is entitled Entropy and Statistical Dynamics.

The second law of thermodynamics works because of the statistics of very large numbers. Consider a bouncing ball: as it bounces, it dissipates heat and eventually does not bounce as high.  

Entropy and Statistical Thermodynamics

This post is part of a series, Nonsense and the Second Law of Thermodynamics. The previous post is entitled The Second Law and Swamp Coolers.

A previous post discusses the macroscopic thermodynamic definition of entropy, but there is another, statistical way of describing entropy.  Consider an isolated macroscopic system of interacting molecules.  Without knowing much about what is going on with the individual molecules, it is possible to measure macroscopic thermodynamic properties such as the pressure, the temperature etc.

                                                                                         (Figure Source)

Consider that the system is isolated; so that the total energy of the entire system of molecules is a constant.  Energy is free to move from one molecule to another, and each molecule has multiple electronic, vibrational, rotational, and translational energy states that it could be in.  There are many distinguishable ways that the system could be arranged to achieve the this energy.

The Second Law and Swamp Coolers

This post is part of a series, Nonsense and the Second Law of Thermodynamics. The previous post is entitled Heat Can Be Transferred From a Cold Body to a Hot Body: The Air Conditioner.

When I was an undergraduate, I had a physical chemistry professor who claimed that air conditioners that were completely inside a room could not possibly work.  Opening the refrigerator door on a hot day will not make your house cooler.

The refrigerator gives off more heat than it transfers from inside itself; a refrigerator is actually heating the house.  If the door is left open, the refrigerator works harder to try to maintain a cool temperature in accordance with its thermostat setting.  As the refrigerator works harder, it releases more heat into the house.

My professor, however, was not correct.  It is possible to have a cooling unit that does more cooling than it releases heat to the environment.  The trick with indoor coolers is that the process by which they operate is not cyclic.