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Latent Heat of Fusion, Specific Heat, & Climate Change

by Eric Hall

February 2, 2013

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Donate I want to start by explaining a concept from physics known as latent heat, specifically the latent heat of fusion. Latent heat is the energy involved when materials change their phase, meaning they go from one form of a solid, liquid, or gas to another. The latent heat of fusion is specifically the amount of energy in the form of heat is absorbed by a material when a solid changes to a liquid. In order to melt 1 gram of ice into water, it takes 334 Joules of energy. There is notemperaturechange during this transition - the 0°C ice becomes 0°C water after absorbing all of that heat.Keep in mind it takes about 4.2 Joules to heat a gram of water by 1C°. It is pretty easy to see that it takes nearly 80 times the energy to melt water as it does to then heat it by 1C°. Or to put it another way, the energy it takes to melt ice could heat a massequivalentof water by nearly 80C°.

The other concept important to note it one of specific heat and the related heat capacity. Specific heat is the concept of how much energy it takes to heat something (or how much energy it gives off in cooling). As mentioned previously, it takes about 4.2 Joules to heat just a single gram of water by 1C°. For comparison of the mass, a tablespoon of water is about 15 grams. So it takes 63 Joules to heat a tablespoon of water by 1C°. To give an idea of how that energy compares, it takes about 0.7 Joules to heat up a gram of sand 1C°, steel about 0.47 Joules, and gold about 0.13 Joules. In other words, water is not easy to heat up or cool off compared to most other materials. And that brings us to the concept of heat capacity. Heat capacity is how much energy it takes to heat up a whole object. For example, the heat capacity of a tablespoon of water is 63 Joules/C°. In heat capacity, you are basically describing the specific heat as well as the mass of the object. This is why it takes so much energy to heat the oceans, because the heat capacity is so large. This is due both to the mass of the oceans as well as the large specific heat of water (in comparison to other materials).

I wanted to start with these concepts because of a news story about a new Norwegian study that shows the warming that will occur due to a doubling of CO2 will be about 1.9 C°. This used the same model they used in 2000, where they predicted about a 3.7C° increase. This makes the data intriguing, because they used a consistent model, and by simply adding the last decade's worth of data into the model, this was the new output. It is only one model, but so far from what I can tell it seems reasonable. There are, however, a few shortcomings.

One important factor I don't see addressed by their model is the solar activity.Temperatures didn't go up as fast in the last decade as most scientists predicted, but there was also a very unusual solar minimum. In fact, the ocean was absorbing much less energy than usual in the period from 2005-2010. The ocean is where most of the energy trapped by the Earth's greenhouse gases ends up. Interestingly, satellite data on solar output showed a decline over that time period and matched very well with the decrease in the amount of energy absorbed by the ocean.I will be interested to see what those in the field have to say about it in the coming weeks after they have had time to review the study.

However, once one considers the role of water and ice into the energy equation, there should be a little doubt as to whether a prediction of airtemperaturesare the best measure of how our climate is really being affected.Temperatures can give us a good estimate of how much energy is being trapped on Earth, but we need to look at the whole system. We must also consider the melting of ice, which as I pointed out at the beginning of the piece, absorbs a huge amount of energy without changing the temperature by a single degree.

One group doubting human caused climate change is a group known asThe Right Climate Stuff. This is a small group of former NASA engineers and scientists who say that CO2 has little or no effect on climate and that almost all of it is natural variation. This is wrong. The physics of CO2 has been well known since the 1950s. It absorbs several wavelengths in the infrared spectrum. When we look at the blackbody curve of the Earth's emitted wavelengths, one of the widest absorption bands for CO2 falls right within the peak wavelengths being emitted by Earth (see figure 1 below - thanks to "the Air Vent" for the figure). It doesn't matter where the CO2 comes from, it means that every singlemoleculemore of CO2 in the atmosphere gives a greater chance of a photon of infrared radiation being absorbed and re-emitted back to earth rather than escaping to space.

Another claim made by "The Right Climate Stuff" makes is their research and "publication" history including their own "report" on climate. Much like otherAnthropogenic Global Warming (AGW) skeptics, none of their reports or studies ever make it to scientific journals, where other scientists can properly debate their methods and quality. In fact, a look byJames Lawrence Powell at 13,950 peer-reviewed climate articles showed only 24 of them reject global warming. If the science is good, scientists who have a well studied hypothesis should go through the process of publishing their data and their analysis so the process of science can take place.

Investors Business Daily made a short list of the main points of"The Right Climate Stuff" group in a bulleted list. I will mention each one and briefly explain how they are partially correct and yet very misleading.
  • To begin with, the group has determined that "the science that predicts the extent of anthropogenic (man-caused) global warming is not settled science."

As the new Norwegian study shows us, this is partially true. The key word here is extent. The CO2 we are generating is causing some of the warming. We know the solar activity plays a role - because that is the source of the energy. We also know the models aren't perfect, and don't always get how warming will affect cloud cover, ocean circulation, and other drivers of climate perfect. However, they get it pretty good and have made good predictions. We are at the point of refining those models - that is where the disagreement is, not as to whether or not warming is happening.
  • Second, the group says "there is no convincing physical evidence of catastrophic anthropogenic global warming."

This is also true. Warming is not going to cause an immediate disaster like an earthquake or an asteroid impact. The effects are much slower. However, they can becatastrophic when accumulated over time. That is really the question - should we do nothing and try tofight off the eventual outcomes as they happen, or be more proactive and try to prevent the eventual damage that will happen? In fact, damage already has happened. New York Harbor has risen over a foot in the last century. AsCynthia Rosenzweig of NASA's Goddard Institute for Space Studies states:
[Superstorm Sandy] itself we can’t immediately link to climate change, but the flooding damage we can. As sea levels continue to rise, a storm of the same magnitude will cause even greater damages due to storm surges coming in on top of a higher “baseline” water level.
Sea levels will rise. Again there is some debate as to how much (depending on the model), but the ice is melting and making the sea rise. The sea also expands as it gets warmer. Hundreds of millions of people in the world live near sea level. Most of them will be able to get away as the rise won't be instantaneous (unless caused by a storm). But how will the world economy absorb this dramatic shift of people? Cities like Miami and New York could end up with water in the streets. Are we prepared for that long-termcatastrophe?
  • Third, it believes the "computer models need to be validated before being used in critical decision-making."'

The models are not perfect. However, all of the models predict both temperature and sea level increases. This means they are on the right track. Should we take the numbers or dates as perfect? Of course not. Let's continue the research and make them better. But based on the trend of all the models, it would be imprudent to ignore them completely. The debate is in the amount of warming and sea level changes, not as to whether or not it will happen. The models show a trend that has been proven correct - and a majority within their error bars. Thus, they have been validated.
  • Fourth, the scientists and engineers also argue that "because there is no immediate threat of global warming requiring swift corrective action, we have time to study global climate changes and improve our prediction accuracy."

This is a weird statement. Because many of the processes of climate change are delayed or lagged, there is a threat of which we might not yet see an effect. As shown earlier, the ocean has a massive heat capacity. Much of the energy being trapped is then stored in the ocean. This energy can then later be responsible for melting ice, changing ocean currents, or several other effects. This can lag by years. While I agree we shouldn't make a hasty decision that is costly and perhaps not helpful, there is no reason to sit and wait to see if the Earth is warming. It is warming. Instead, it is time to look at technologies that can help reduce CO2 and other ways to become more efficient.
  • Finally, they say that Washington is "over-reacting" on global warming and suggest that a "wider range of solution options should be studied for global warming or cooling threats from any credible cause."

My personal opinion is Washington DC suffers from the same problem as many corporations do in the modern era. There is no thought to the long-term, only the next election or the next quarter. Washington over-reacts because its politicians wants to make a political statement, not actually confront the problem. There has been plenty of waste in the name of stopping AGW. But just because not all plans in the past have been good doesn't mean we shouldn't try to make better plans going forward.

There is also an additional battle that climate scientists face when trying to explain the science of AGW. There is still a segment of the population that doesn't trust the process of science. For example, this post from a Christian news site links AGW and Darwinism, claiming both are false:
Darwinists often sound just as authoritive...We shall find interesting similarities between Darwinian rhetoric and the persuasive strategies of catastrophic anthropogenic global warming (CAGW) advocacy.
The piece goes on to cite other reports that the warming is not quite as high as earlier model runs suggested, but never actually show it isn't happening at all. Even more interesting, they actually cite aNational Center for Science Education project where they had clergy sign on to a statement regarding science education and reconciling it with the bible. Part of the statement reads:
We the undersigned, Christian clergy from many different traditions, believe that the timeless truths of the Bible and the discoveries of modern science may comfortably coexist. We believe that the theory of evolution is a foundational scientific truth, one that has stood up to rigorous scrutiny and upon which much of human knowledge and achievement rests. To reject this truth or to treat it as “one theory among others” is to deliberately embrace scientific ignorance and transmit such ignorance to our children. We believe that among God’s good gifts are human minds capable of critical thought and that the failure to fully employ this gift is a rejection of the will of our Creator. To argue that God’s loving plan of salvation for humanity precludes the full employment of the God-given faculty of reason is to attempt to limit God, an act of hubris.
However, the author uses a little hand wave to totally dismiss the position:
Although there are elements of truth in this statement, most of these clergy are simply taking it on faith that the Darwinian establishment has "overwhelming evidence" for its position. But such faith is not supported by the actual scientific evidence.
It baffles the mind that someone cannot understand the overwhelming scientific evidence on something such as evolution. Yes, the theory has continued to be refined as we learn more and fill in the gaps of the fossil record. But the theory has made many predictions for which scientists later have found fossils to match. This cross-section of the population doesn't understand the basic process of science, especially ones that encompass large ideas such as evolution or planetary climate. I'm not sure how to reach these people.

In the end, even the basic science should tell us the Earth is going to warm. CO2 traps the wavelengths emitted by the Earth really well. The energy required to melt ice and warm water can mask some of the energy imbalance as they have high values in their latent heat and heat capacity. If we could just get past that basic hurdle and then have a reasonable discussion about the amount of warming and the possible impacts and how to plan for them, it would be huge progress. Perhaps we do nothing and instead adapt (not my opinion, but it is an option). Maybe we act quickly and heavily tax all carbon (also not a good idea). Or perhaps we look to new technology and better predictions to better plan for what we will face the next 100 years. Whatever the next step is, let's get off the first step of ignoring the basic science of a warming Earth.

by Eric Hall

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