There are two things that I associate with the Fall season: Halloween and raking leaves.  While the former brings out my inner child who yearns for costumes and candy, the latter is the focus of this article, as it provides a wonderful illustration of the second law of thermodynamics.

Ah, the second law... Personally, I have never been particularly drawn to the study of thermodynamics, but I have always had an affinity for the second law and all of its fascinating philosophical implications.

The zeroth law of thermodynamics discusses thermal equilibrium, and in so doing, gives meaning to the term temperature.  The first law describes the conservation of energy, and dictates that energy cannot be created nor destroyed.  The second law says, in a variety ways, that no system can be 100% efficient, and as such, every system has losses. 

If you are curious, the reason that there is a zeroth law is that it was developed decades after the first two, but precedes them in terms of scientific principle, in that it lays a foundation for further study.  Rather than shift laws one and two up to two and three, it was decided that they be left alone, and that the new law be referred to as law zero.  This was a great choice, because it gave scientists the opportunity to use the term "zeroth", and as a result, sound very intelligent.

In summary, law zero says there will be lunch, law one says that it will not be free, and law two says that actually, you have to tip.

While the zeroth and first laws of thermodynamics set up a structure for studying energy and temperature, the second law gets the wheels turning, by offering something somewhat unusual for science: direction. 

The simplest statement of the second law is that heat travels spontaneously from hot bodies to cold ones.  That is, the heat from a steaming cup of coffee leaves the liquid and travels to the cooler surrounding air in the room.  This simple statement, so obvious in nature, gives rise to some of the most profound concepts in science. 

No one would think for a moment that additional heat from the room would spontaneously transfer to an already scolding cup of coffee.  That would be like an already wealthy person taking additional funds from someone who is financially constrained.  Though such an occurence is not unsual within society, it is a road seldom taken by our equitable mother nature.  The second law states that such a clear disregard for equilibrium is so improbable, that it is illegal.  In nature, everything searches for equilibrium. 

Let us take the air in a classroom for example.  What are the chances that all of the particles that make up this volume of air will spontaneously shift to one side of the room, leaving a vacuum on the other side of the room (and causing terrible consequences for those students left in a vacuum of space)?  The probability of this occuring is so low, that we may simply conclude that it is nil.

Let us now reverse the problem.  If one were to manually displace all of the air particles in the classroom to one side, what would happen if they were set free?  If the air were left to its own devices, it would immediately try to balance itself in the given space.  The air would naturally disperse to fill the volume with air of equal pressure and temperature (assuming that the boundaries encompassing the space are uniform).

One might refer to the original state, where all of the particles are grouped together at one side, as 'organized' or orderly.  The second situation, where the air is evenly dispersed, could then be deemed disorganized or disorderly.  We could even call this dispersed situation 'random', or even better, 'chaotic'.

It turns out that scientists like to measure everything, including randomness.  In thermodynamics, the quantity of chaos is called entropy.  A very chaotic, disorganized state, is one with high entropy, whereas a very organized system has low entropy.  Entropy is a measure of energy per unit temperature, or Joules per degree Kelvin (J/K).

Returning to the dispersing air within a room, we could conclude that the original, organized state had little entropy, while the random state, that it naturally tended towards, is one of high entropy.  So, the notion that heat moves from hot bodies to cold ones leads directly to the idea that the entropy of a system increases with time.  A kindergarten teacher can leave a room full of children calmly sitting at tables colouring, and return to complete pandemonium in just a few minutes.  A closed system tends towards chaos: it is the second law.

So, how does this relate in any particular way to the Autumn season?  I'm glad you asked.

Last week, I was raking leaves with my two-year-old daughter.  After organizing the leaves into distinct piles, it was time for her to jump in them.  After a half an hour of fun, I wanted to place the leaves in bags - my daughter, a lovely but at times possessive little girl, objected to the removal of her piles.  I conceded, and left the piles of leaves as they lay, with the intention to return to bag them at a later time, when one particular little girl was napping.

When I did return with bags, I noticed that the orderly piles had become randomly distributed around the lawn by wind.  The organization of the leaves decreased, that is, the system of leaves increased in entropy.  The opposite would never happen.  One would never expect the wind to organize a randomly dispersed collection of leaves into clean piles.

As I raked the leaves into piles, again, and finally disposed of them, I thought of the second law of thermodynamics.  The only way to bring about an increase in the organization of a system is to interfere with it.  However, we must realize that when we do so, we become part of the system.  The total system, consisting of the leaves, the rake, and my body, experiences an overall increase in entropy.  I may, philosophically speaking, decrease the entropy of the leaves, but my concerted, non-spontaneous effort to do so requires an input of energy on my part, which causes my body temperature to increase.  Overall, there is a net increase in entropy; there always is.

When I originally introduced the second law of thermodynamics, I stated it another way: no system can be 100% efficient.  It turns out that a system that gains entropy has an inherent inefficiency associated with it.  And since every system gains entropy with time, no system is perfectly efficient.  This gives rise to yet another statement of the second law: there is no such thing as a perpetual motion device. 

Every system has at least some loss associated with it.  No contact is perfectly frictionless.  A pendulum swaying back and forth will, after enough time, come to rest.  Its mechanical energy will eventually all be converted into heat.  The notion that no body can undergo perpetual motion is easy to relate to - we all need to rest.  One spinoff that is not so rosy, but is equally true, is that nobody can live forever.

But you know, the second law can work for us under certain conditions... The next time someone calls you lazy, just remind them that there is no such thing as a perpetual motion device.

The final statement of the second law is easily the most compelling, as it imposes a constraint on time itself: time can only flow in one direction.   

Imagine you are shown two pictures of a billiards table.  The first picture shows fifteen coloured balls organized into a triangular shape with the white ball on the opposite side of the table, while the second has all of the balls placed randomly around the table.  You could confidently ascertain that the second picture was taken after the first without even watching the game.  How did you know?  Since an increase in randomness occurs naturally as time moves forward, the second law goes so far as to stipulate the direction of time's arrow.

Most principles in science have a certain symmetry to them, that is, they look the same no matter how you view them.  The second law of thermodynamics is special, because it implies that things move in one direction only.  The notion of permanent change is rather unsettling, but we must accept the fact that our universe will have more entropy tomorrow than it did today.  The second law proves that in life, there is no undo button.

The harsh reality is that the decisions we make in life cannot be unmade.  And, if left unchecked, things naturally tend towards a big mess.  It may take months to paint a masterpiece, carefully placing each grain of colour in just the right spot.  It takes only minutes for the painting to be ruined by rain if left outside. 

Thankfully, we can restore order to chaotic situations if we are willing to put in the work.  Such actions raise our body temperature, which is welcomed now, but is embraced even more during the season that lurks around the corner.

There are several laws of thermodynamics, all of which have applications across the various scientific fields.  These laws also have deep philosophical implications, with the second law leading the charge in this regard.  I have already written two articles describing the first law (energy balance).  I will soon cover the depths of the second law, but I feel the need to discuss the most fundamental law beforehand.  Strangely enough, there is a law that comes before the first law.

 

The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with an external system, then they are also in thermal equilibrium with one another.  Thermal equilibrium means that heat is not being exchanged between two systems.  When two systems having different temperatures come into contact with one another, they will inevitably experience heat transfer.  Once thermal conduction is complete, the collective system will arrive in thermal equilibrium.

A natural offshoot of the zeroth law is that if two surfaces baring different temperatures should come into contact, they will eventually both arrive at a common temperature, which lies somewhere between the two initial ones.  Put mathematically, if surface A with temp A presses up against surface B with temp B, both surfaces A and B will have temp C after some time such that temp A<C<B.  In a philosophical sense, the two systems will rub off on one another, or compromise, and find themselves altered, and after some time, identical, from a thermal energy standpoint.

The situation is analogous to what happens when two different cultures co-exist in a given environment.  When cultures mix in a defined space, all cultures involved tend to experience change as a result.  Non-Christians in North America, for example, are in the relative minority, and must endure Christmas music whenever shopping in December.  In the province of Quebec, the language of majority is French, and Anglophones who live there are certainly impacted by the cultural differences associated with the language differences.

In the end, a middle ground tends to be forged across cultures.  In Quebec, for example, businesses are allowed to have English signs, just as long as they have a smaller font size than the French ones.  Out-of-towners may think this is a joke, but there is actually a defined ratio between French to English font-size that is enforced.  As a resident of the province, it can sometimes feel like a mild dictatorship.

When two different surfaces come into contact, the temperature that is agreed upon is not necessarily half way in between the two initial ones.  If one surface belongs to a significantly larger body, the final temperature that is agreed upon will be closer to it than the small body that is causing the change.  In Star Wars, when a small ship strikes the death star, the death star is affected, but barely.  It is the same in society.  The larger culture tends to bend the smaller ones.  They may experience some change, but the smaller ones risk being eaten.

The big fear among cultures, particularly minority cultures, is assimilation.  Cultural assimilation implies the death of a culture, as its original life force would be lost.  Smaller religious groups, like Judaism, fear nothing more than dying out, being absorbed over time by more massive religions.  This is one reason why intermarriage is frowned upon by religious communities (particularly smaller ones).

 

The point that is not appreciated by religious leaders is that the cultural differences across different religions can make the human race collectively stronger.  It is the lack of acceptance throughout divided nations that threatens to divide it further.  Intolerance is the match that lights cultural differences aflame, and leads to a blaze of hate, which in a place like Israel, has burned for decades.

When cultures clash in a violent way, we can think of it as an act of heat transfer – two systems in search of thermal equilibrium.  Beware: a permanent state of equilibrium is a dangerous thing to search for, because it is our differences that define us.  They keep things fresh, offering different perspectives.  If one culture were to overtake all others, there would be no culture left.  Total assimilation is a bad thing.  Like the zeroth law says, identical temperatures do not exchange heat.  Similarly, commonality across all cultures would end the exchange of ideas, and in turn, slow progress.

 

It gets much worse.  The zeroth law implies that the universe would die out eventually were it not expanding quickly enough.  Were the universe to exist in a defined, enclosed space, all of the matter it contains would arrive at the same temperature sooner or later .  This would certainly represent the end of life in the universe, as without temperature gradients, the chemical and physical reactions that support life could no longer occur (not to mention the fact that the average temperature in the universe is currently around -270 degrees Celsius).  A thermodynamically bland universe is the death of the universe, and a bland society represents societal death.  Cultural differences are the spice of life.

It seems that sharing land will always require that compromises be made.  It would be nice though, if the mode in which these inevitable conflicts are resolved were respectful.  Think of the harmony of the zeroth law, as when a father warms his daughter’s hands by covering them with his own.  The skin in contact does not ask if it is fair to be exchanging heat.  It does not complain.  It simply follows the law.  People, on the other hand, are more complicated than the cells of which they are made – but that does not mean that they cannot learn from them.

December began with an article that related a healthy lifestyle to the first law of thermodynamics.  The first law says that the quantity of energy contained within a system must be conserved – never created or destroyed.  In relation to dieting, the lesson we may draw from this is that the amount of energy that we consume should be kept in check with respect to the amount of energy we output.  Short of bariatric surgery, we must output more than we input for our body to lose weight.

Let us now take a closer look at the first law of thermodynamics.  The conservation of energy principle has more to teach us than merely how to balance energy.  The law also establishes the concept of mechanical work.  Before getting into the physical definition of work, let us examine the traditional kind of work that we are all familiar with, like jobs and chores.

 

Have you ever heard a tough and hardened individual say, “You could learn a lot from a hard day’s work?”  We get more out of life when we put more into it.  As we will see, the benefits of working hard are actually predicted by the first law of thermodynamics.

I have observed the benefits of hard work as a student, a working engineer, and as a teacher.  I always seem to derive more pleasure from my life when I allow my spirit to enter into my work.  If I give myself to my work, I always seem to be rewarded for it.  I do not mean that I get higher marks in school or a raise at work.  Those things can and sometimes do happen, but something else even more important occurs in parallel.

Simply put, you feel good when you do a good job.  Good marks, good pay... they are relished more when they are merited.  Even when hard work is not rewarded in a tangible way (this is the standard for educators in North America), the work a person puts into something is its own reward.  Much the way the body releases endorphins when physical work is done, accomplishing a task causes instant gratification in the brain.

To illustrate the inherent value in doing good, hard work, I want to share something a bit personal.  In my recent experience as a teacher, I have seen some lows followed by some highs.  This past January, the winter semester of 2010, I began teaching physics at the college level.  I looked at the course outline, and set out to teach the course requirements.  I did my job, maybe even a good job, but I did not invest myself into it.  After all, I was not certain at the time whether teaching would be a short-term or long-term profession for me.  The semester went by, and in the end, I felt that teaching was a bit of a drag.  Was it because the students were too lazy?  Was the material too boring?

I did some soul searching in the summer that followed, and debated a return to engineering.  However, when the autumn semester rolled around, I opted to give teaching another go.  This time around, I told myself that I would commit to the teaching profession for a few years.  This commitment led me to prepare excellent course notes, since I knew they would be reused in future semesters.  The better notes led to better lectures, and the students clearly benefitted from that.  I felt better about the semester too.  I received no monetary raise, but my job satisfaction increased nonetheless.  I am now looking forward to my next teaching opportunity.

It turns out that some of the students were a little too lazy, and yeah, some of the introductory material was boring, but neither of these issues account for the drastic difference in my teaching experience from one semester to the next.  The problem in the first semester was my level of personal investment.  I worked harder throughout the semester that followed, and that made all the difference.

Physicists describe mechanical work as the amount of energy added to a system by an external agent, which applies a force over a given distance.  The simplest example of this is my hand pushing a block across a table.  If I apply a constant, 1 Newton force with my hand onto the block parallel to the table on which it slides, along a 1 metre distance, I will be applying 1 Nm (Newton Metre) of work to the block.  A Newton Metre is actually a Joule, which is the standard unit for energy.  It turns out that mechanical work and energy are transferrable entities.  The work I apply to the block gives it kinetic energy, or the energy associated with its motion.

Let us describe my classroom experience as a block sliding along a table.  The most direct way to add energy to any system is to apply positive work to it.  If I push the block with more force for a longer distance in its direction of motion, I will apply more positive work to it.  It follows, that if I work harder, then the block will slide further (i.e. the students will learn more), and more friction will be generated between the block and the table as a result.  This additional friction will cause the system to create more heat than it otherwise would have, generating more classroom discussion.

The block may arrive at its intended destination in a number of ways.  Some people may try to cheat by tilting the table or pouring ice over it.  Sure, both tactics may allow the job to get done, but both keep the block at a distance.  Direct, hard work, is usually the most efficient kind.  It ensures that the work gets done, and that you get a front row seat to examine the progress of the block.  There is no better feeling as a teacher than when a struggling student achieves success because he or she has been inspired to learn.

There are many kinds of work that a person can do.  Sometimes, the most gratifying kind is pure and simple physical labour.  I like camping trips.  You get up, you feed your body energy, you output work all day, sleep and repeat.  I like moving days too.  What could be simpler?  Take this pile of stuff and transport it from here to there.  I believe that the pizza and beer tastes better for the friends who actually do the heavy lifting than for the friends who show up but don’t really help much.  Furthermore, I don’t think that a meal cooked by someone else tastes better.  No one enjoys the food more than the chef.

Sometimes, a person who feels lazy may have a hard time to get going.  Once they do, they will probably realize the joy of work.  It may take a long time for a person to appreciate this.  The concept can be instilled quickly in certain work-intensive environments, like, for instance, a military training base. 

In today’s work environment, one can expect to be pushing the block up a steep incline.  Without a significant input of work, no progress will be made, and one will find oneself unemployed.  The ability to perform work, to accomplish a task, truly is a privilege.  Take it from this tough and hardened teacher.   

*** Disclaimer: While the laws of thermodynamics apply unconditionally to everyone, I am no dietician, and so my proposed law of dieting is based on opinion, and may not apply to all dieters. ***

The holiday season is upon us, and there are two things we can expect with certainty once December is complete: (1) 2010 will become 2011, and (2) in the month of January, we will be inundated with new dieting suggestions. 

A quasi-doctor with nice teeth and salon-fresh hair will push her new-age plant diet, which involves eating anything in your home that grows from Earth.  A very muscular chiropractor who graduated from I-Wish-I-Was-A-Dr. University will counter this ad with his “Nothing but Brownie” diet, which promises to make each of your bowel movements smell like Parisian baked goods.   

Many of us consume more Calories than usual during the cold holiday season.  Then, we make the unrealistic New Year’s resolution to transform from couch potatoes into gym nuts as the clock strikes midnight on December 31^st.  Some people follow through with their plans to exercise more, but most do not, as is evidence by how busy gyms are in January versus March.  Some people who give up on their exercise plans take solace in the fact that they are still eating a magical cookie for breakfast and lunch; they get oatmeal raisin Monday to Thursday, but chocolate chip on Friday.  On the weekend they are rewarded with non-cookie items, just as long as they think of cookies while they are being consumed.

It may all seem ridiculous, and that is because it is.  There is a lot of false science out there, but few domains of science contain more myths and misinformation than that of nutrition.  It is a shame, because at the root of diet and exercise is one very simple scientific law that, if considered, can solve the issues pertaining to weight and overall fitness for the majority of the population in developed nations.

It is known as the First Law of Thermodynamics, which may sound complicated or scary to someone with distaste for science.  This law states that energy can be neither created nor destroyed, only converted from one form to another.  In the simplest case, that of a closed system, we can easily appreciate this law at work.  It is somewhat more complicated for the human body, but the “First Law of Dieting” is simple: if you wish to lose weight, you need to burn more energy than you consume. 

Let us first consider the closed system of a wooden block sliding along a flat, rough surface, like a table.  We will place a dome over the table, and call the system a closed one consisting of the table’s top surface, a wood block in motion, and the air under the dome.  Initially, the block has a lot of kinetic energy due to its speed, and everything in the closed system is at room temperature.  At a later point in time, say, two seconds later, the block has slowed down due to friction between it and the table.  Less speed means less kinetic energy.  So, where did the energy go?  It was not destroyed, for this would defy the first law of thermodynamics.  It was converted, due to friction which worked against the direction of motion, into heat. 

Indeed, the surfaces in contact, the bottom surface of the block and the path of the table it slid across in that time, have increased in temperature.  The sliding process caused the kinetic energy to be converted into heat.  The path of the table eventually cools off, but the air under the dome heats up slightly as a result.  At any moment in time, the total mechanical energy of the system is conserved.

While the human body is encapsulated by a large dome or bondary (skin), the skin itself is full of holes, or pores.  Regarding energy and mass transfer, there are three other relevant openings to the body (orifices): one inlet, known as the mouth, and two outlets that work best near toilets.  Due to all of these openings, the human body may be viewed as an open system.  The first law applies to open systems as well as closed ones so long as we account for all that comes in and goes out.  In addition to the energy conservation law, the mass passing through and maintained within the system must also be conserved (not created nor destroyed).  These conservation laws are actually quite simple.  They work like your cheque account at the bank.  No money is created, and hopefully none is destroyed.  If your account has $200, and you deposit $50, you can take out no more than $250.  Furthermore, the teller at the bank will never remind you to stop filling your account.  Expanding accounts is good, while expanding waistlines is often not.

All foods have a certain caloric value associated with them.  Let us take Multi-Grain Cheerios for example, for which one serving (30 grams) corresponds to 120 Calories.  The “Calorie” is a false unit of energy when used to describe food products, as the true “calorie” (non-capitalized) is the amount of energy it takes to raise the temperature of one gram of water by one degree Celsius.  The Calorie on the side of your cereal box actually refers to kilocalories (1 Calorie = 1000 calories).  Engineers use Joules (J) as the standard unit of energy, and they refer to the amount of energy required to accelerate a 1-kg block by 1 m/s² along a frictionless surface over a 1 metre length.  One calorie is equal to 4.184 Joules, so my thirty grams of cereal (without milk) corresponds to 120,000 calories or 502,080 J, or about 500 kJ.

When I consume this amount of cereal, the total amount of mass and energy in my body increases by 30 g and 500 kJ, respectively.  The food is then in for quite a trip.  Bypassing the details, some of the nutrients are kept, and some are discarded by the body as waste.  More mass enters than leaves, and so, the mass of the body increases ever so slightly.  Fortunately, pores are another place where mass, in the form of fluid, can leave the body.

Many people do not realize this, but a large percentage of the total energy taken in when eating is spent during the digestion process.  This is why we often feel exhausted after a big meal.  Some buffet restaurants actually have beds for rent adjacent to the dining room ... OK, I made that up, but the idea could take off one day considering North American eating habits.  We are unaware of much of the energy that our body spends.  Our hearts beat, our lungs inflate, and our neurons fire; each of these involuntary processes require energy.  Still, if we lead a stagnant life, completely devoid of voluntary muscle contractions, ie, exercise, we will voluntarily take in more energy than we involuntarily use, and invariably gain weight over time.  Adding a couple of pounds per year for twenty years transforms a healthy twenty-year-old into a forty-pound-overweight forty-year-old; this is known as the middle-aged bulge.

The overall message I mean to deliver is that if possible, we ought to consume a rational amount of food, which corresponds to a rational amount of energy.  If you will spend the afternoon camping, skiing, or helping a friend move heavy boxes, then a calorie-rich lunch, consisting of a double-portion of lasagne (1000 Calories, or 4184 kJ) makes sense.  However, if the afternoon is spent typing in your seat at a computer, then 400 Calories from a salad and a slice of bread should do you just fine.  The alternative meal choice, the double-portion of lasagne, would quickly find itself floating around in your buttocks region. 

An individual with average weight who leads a reasonably active lifestyle (moderate intensity cardiovascular activity for thirty minutes five times per week) should consume roughly 2,000 Calories per day.  Athletes require more like 4,000, but those who watch athletes do not.  If you want to lose weight, you need to reduce caloric intake and increase voluntary activity.

The above paragraph is a good guideline.  I suppose that so many of us invest our time and money into cookie diets and other fads because we want to believe there is an easier solution than rational diet and exercise.  Of course, my 30 grams of cereal contains more information than the energy content, but none are nearly as important.  I don’t mean to belittle the Nutrition industry, who is very interested in fats, carbs, proteins, and vitamins.  These aspects of food are important, but for most, they are of secondary importance.  The science behind nutrition is much more complicated than the simple conservation laws I have described.  Still, we are left with the question, “What should I eat?”  For this question, I will offer a rule of thumb that I heard of some years ago: “Eat food, not too much, mostly plants.” 

As for the Dieting industry, I have every intention of belittling it.  It is one of many industries that would be crushed if the general population were both well-educated about nutrition and disciplined.  But it’s December, and it is much easier to eat that second piece of pie, I mean, it’s just sitting right over there!  Get in my belly!