The Second Law


PW Atkins' beautiful book, The Second Law, defines what the second law means and how it impacts every facet of the world and our lives

The Rabbit Hole is written by Blas Moros. To support, sign up for the newsletter, become a patron, and/or join The Latticework. Original Design by Thilo Konzok.

Key Takeaways

  1. The Laws of Thermodynamics
    1. The name thermodynamics is a blunderbuss term originally denoting the study of heat, but now extended to include the study of the transformation of energy in all its forms. It is based on a few statements that constitute succinct summaries of people's experiences with the way that energy behaves in the course of its transformations. These summaries are The Laws of Thermodynamics. Although we shall be primarily concerned with just one of these laws, it will be useful to have at least a passing familiarity with all of them. There are four laws. The third of them, the second law, was recognized first; the first, the zeroth law, was formulated last; the first law was second; the third law might not even be a law in the same sense as the others
      1. Zeroth Law
        1. The zeroth Law was a kind of logical afterthought. Formulated by about 1931, it deals with the possibility of defining the temperature of things. Temperature is one of the deepest concepts of thermodynamics, and I hope this book will sharpen your insight into its elusive nature. Simply, around thermal equilibrium and 
      2. First Law
        1. The first law is popularly stated as "energy is conserved." 
      3. Second Law
        1. The second law recognizes that there is a fundamental dissymmetry in Nature: the rest of this book is focused on that dissymmetry. All around us are aspects of that dissymmetry: hot objects cool, but cool objects do not spontaneously become hot; a bouncing ball comes to rest, but a stationary ball does not spontaneously begin to bounce. Although the total quantity of energy must be conserved in any process, the distribution of that energy changes in an irreversible manner. The second law is concerned with the natural direction of change of the distribution of energy, something that is quite independent of its total quantity
        2. Energy drops from the hot source to the cold sink, and is conserved; but because we have set up this flow from hot to cold, we are able to draw only some energy off as work; so not all the energy drops into the cold. The cold sink appears to be essential, for only if it is available can we set up the energy fall, and draw off some as work. In every engine, there has to be a cold sink, and that at some stage of the cycle energy must be discarded into it. That little mouse of experience is nothing other than the second law of thermodynamics. All the law seems to be saying is that heat cannot be completely converted into work in a cyclic engine: some has to be discarded into a cold sink. That is, we appear to have identified a fundamental tax: Nature accepts the equivalence of heat and work, but demands a contribution whenever heat is converted into work. Note the dissymmetry. Nature does not tax the conversion of work into heat: we may fritter away our hard-won work by friction, and do so completely. It is only heat that cannot be so converted. Heat is taxed; work is not. 
          1. No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.
          2. Similarly, no process is possible in which the sole result is the transfer of energy from a cooler to a hotter body (flow from cold to hot is possible but not natural. Only the spontaneous shift of heat from cold to hot without there being change elsewhere is against nature..)
          3. Natural processes are accompanied by an increase in the entropy of the universe.
        3. The domain of the second law is corruption and decay
        4. One of the most important contributions of 19th century thermodynamics is our comprehension that work and heat are names of methods, not names of things...Both heat and work are terms relating to the transfer of energy. To heat an object means to transfer energy in a special way (making use of a temperature difference between the hot and the heated). To cool an object is the negative of heating it: energy is transferred out of the object under the influence of a difference in temperature between the cold and the cooled. It is most important to realize, and to remember throughout the following pages, that heat is not a form of energy: it is the name of a method of transferring energy. The same is true of work. Work is what you do when you need to change the energy of an object by a means that does not involve temperature difference. Thus, lifting a weight from the floor and moving a truck to the top of a hill involves work. Like heat, work is not a form of energy: it is the name of a method for transferring energy. 
        5. Work into Quality
          1. Suppose we have a certain amount of energy that we can draw from a hot source, and an engine to convert it into work. We know that the second law demands that we have a cold sink too; so we arrange for the engine to operate in the usual way. We can extract the appropriate quantity of work, and pay our tax to Nature by dumping a contribution of energy as heat into the cold sink. The energy we have dumped into the cold sink is then no longer available for doing work (unless we happen to have an even colder reservoir available). Therefore, in some sense, energy stored at a high temperature has a better "quality": high-quality energy is available for doing work; low-quality energy, corrupted energy, is less available for doing work...Just as the increasing entropy of the universe is the signpost of natural change and corresponds to energy being stored at ever-lower temperatures, so we can say that the natural direction of change is the one that causes the quality of energy to decline: the natural processes of the world are manifestations of this corruption of quality
          2. Here is our first major result of thermodynamics: we now know how to minimize the heat we throw away: we keep the cold sink as cold as possible, and the hot source as hot as possible. That is why modern power stations use superheated steam: cold sinks are hard to come by; so the most economical procedure is to use as hot a source as possible. That is, the designer aims to use the highest-quality energy...There appears to be a limit to the lowness of temperature. The conversion efficiency of heat to work cannot exceed unity, for otherwise the first law would be contravened...Absolute zero appears to be unattainable
            1. Hottest possible source, coldest possible sink. This contrast offers the most efficient system
            2. Some deep thread with velocity, friction, superheated sources and super cooled sinks
          3. Quality must reflect the absence of chaos. High-quality energy must be undispersed energy, energy that is highly localized (as in a lump of coal or a nucleus of an atom); it may also be energy that is stored in the coherent motion of atoms (as in the flow of water)
        6. When we do work on a system, we are stimulating its particles with coherent motion; when we heat a system, we are stimulating its particles with incoherent motion
          1. Deep thread with coherence, superfluidity, work 
        7. Thermal equilibrium corresponds to the most probable state of the universe...So long as a process is occurring in which more chaos is generated than is being destroyed, then the balance of the energy may be withdrawn as coherent motion...The state of more chaos can allow greater coherence locally, so long as greater dissipation has occurred elsewhere...Order on any scale can arise from collapse into chaos: order springs locally from disorder elsewhere. Such is the spring of change. 
        8. Chaos determines not only destiny but also the rate at which that destiny is achieved
      4. Third Law
        1. The third law of thermodynamics deals with the properties of matter at very low temperatures. It states that we cannot bring matter to a temperature of absolute zero in a finite number of steps. 
    1. Fluid flows from a hot, thermally "high" source to a cold, thermally "low" sink
  2. Other
    1. Work and heat are mutually inter-convertible, and heat is not a substance like water
    2. An engine is something that converts heat into work. Work is a process such as raising a weight. Indeed, we shall define work as any process that is equivalent to the raising of a weight. Later, as this theory develops, we shall use our increased insight to build more general definitions and find the most all-embracing definition right at the end. That is one of the delights of science: the more deeply a concept is understood, the more widely it casts its net. 
      1. Work is a way of transferring energy between a system and its surroundings; it is a transfer effected in such a way that a weight could be raised in the surroundings as a result. When work is done on a system, the change in the surroundings is equivalent to the lowering of a weight.
    3. The godfathers of the field are Kelvin, Clausius, Carnot, and Boltzmann

What I got out of it

  1. The last half was a bit too technical for me but there were a couple fundamental ideas which were clarified around the second law of thermodynamics. Two of the biggest, for me, are that quality of energy = capacity for work (think this is a fascinating way to think about the elusive idea of "quality") and the idea that the larger the contrast between the hot source and the cold sink, the more efficient the system is (this is an idea which can be applied to every facet of your out contrast..., aka competitive advantage...)

In the Latticework, we've distilled, curated, and interconnected the 750+book summaries from The Rabbit Hole. If you're looking to make the ideas from these books actionable in your day-to-day life and join a global tribe of lifelong learners, you'll love The Latticework. Join us today.