The First Law of Thermodynamics

(Four Laws That Drive the Universe by Peter Atkins)

2. THE FIRST LAW

The conservation of energy

The first law of thermodynamics is generally thought to be the least demanding to grasp, for it is an extension of the law of conservation of energy, that energy can be neither created nor destroyed. That is, however much energy there was at the start of the universe, so there will be that amount at the end.  But thermodynamics is a subtle subject, and the first law is much more interesting than this remark might suggest.  Moreover, like the zeroth law, which provided an impetus for the introduction of the property ‘temperature’ and its clarification, the first law motivates the introduction and helps to clarify the meaning of the elusive concept of ‘’energy’.

We shall assume at the outset that we have no inkling that there is any such property, just as in the introduction to the zeroth law we did not pre-assume that there was anything we should call temperature, and then found that the concept was forced upon us as an implication of the law.  All we shall assume is that the well-established concepts of mechanics and dynamics, like mass, weight, force, and work, are known.  In particular, we shall base the whole of this presentation on an understanding of the notion of ‘work’.

Work is motion against an opposing force. We do work when we raise a weight against the opposing force of gravity.  The magnitude of the work we do depends on the mass of the object, the strength of the gravitational pull on it, and the height through which it is raised.  You yourself might to be the weight:  you do work when you climb a ladder; the work you do is proportional to your weight and the height through which you climb.  You also do work when cycling into the wind: the stronger the wind and the further you travel the greater the work you do. You do work when you stretch or compress a spring, and the amount of work you do depends on the strength of the spring and the distance through which it is stretched or compressed.

All work is equivalent to the raising of a weight.  For instance, although we might think of stretching a spring, we could connect the stretched spring to a pulley and weight and see how far the weight is raised when the spring returns to its natural length. The magnitude of the work of raising a mass m (for instance, 50 kg) through a height h (for instance, 2.0 m) on the surface of the Earth is calculated from the formula mgh, where g is a constant known as the acceleration of free fall, which at sea level on Earth is close to 9.8 m s^-2.  Raising a 50 kg weight through 2.0 m requires work of magnitude 980 kg m^2 s^-2.  As we saw in the footnote on p. 14, the awkward combination of units ‘kilograms metre squared per second squared’ is called the joule (symbol J). So, to raise our weight, we have to do 980 joules (980 J) of work.

(p.14  1. Energy is reported in joules (J): 1 J = 1 kg m^2 s^-2. We could think of 1 J as the energy of a 2 kg ball travelling at 1 m s^-1). Each pulse of the human heart expends an energy of about 1 J.)

Work is the primary foundation of thermodynamics and in particular of the first law. Any system has the capacity to do work.  For instance, a compressed or extended spring can do work: as we have remarked, it can be used to bring about the raising of a weight.  An electric battery has the capacity to do work, for it can be connected to an electric motor which in turn can be used to raise a weight.  A lump of coal in an atmosphere of air can be used to do work by burning it as a fuel in some kind of engine.  It is not an entirely obvious point, but when we drive an electric current through a heater, we are doing work on the heater, for the same current could be used to raise a weight by passing it through an electric motor rather than the heater.  Why a heater is called a ‘heater’ and not a ‘worker’ will become clear once we have introduced the concept of heat.  That concept hasn’t appeared yet.

With work a primary concept in thermodynamics, we need a term to denote the capacity of a system to do work: that capacity we term energy. A fully stretched spring has a greater capacity to do work than the same spring only slightly stretched: the fully stretched spring has a greater energy than the slightly stretched spring.  A litre of hot water has the capacity to do more work than the same litre of cold water: a litre of hot water has a greater energy than a litre of cold water.  In this context, there is nothing mysterious about energy: it is just a measure of the capacity of a system to do work, and we know exactly what we mean by work.  

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Now we extend these concepts from dynamics to thermodynamics.