Author: Atkins, Peter
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Whereas for us the universe is everything, for a less profligate thermodynamicist it might consist of a beaker of water (the system) immersed in a water bath (the surroundings).
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‘Flexible walls’ is best thought of as meaning that the boundary of the system is rigid everywhere except for a patch—a piston—that can move in and out. Think of a bicycle pump with your finger sealing the orifice.
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The zeroth law implies that just as the pressure is a physical property that enables us to anticipate when systems will be in mechanical equilibrium when brought together regardless of their composition and size, then there exists a property that enables us to anticipate when two systems will be in thermal equilibrium regardless of their composition and size: we call this universal property the temperature.
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If no change occurs, then either the temperatures are the same or—if we know that they are different—then the walls are classified as adiabatic (‘impassable’).
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The Swedish astronomer Anders Celsius (1701–1744) after whom the former is named devised a scale on which water froze at 100° and boiled at 0°, the opposite of the current version of his scale (0°C and 100°C, respectively).
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Very occasionally you will come across the Rankine scale, in which absolute temperatures are expressed using degrees of the same size as Fahrenheit’s.
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Classical thermodynamics is the part of thermodynamics that emerged during the nineteenth century before everyone was fully convinced about the reality of atoms, and concerns relationships between bulk properties. You can do classical thermodynamics even if you don’t believe in atoms.
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The precise form of the distribution of the molecules over their allowed states, or the balls over the shelves, is called the Boltzmann distribution. This distribution is so important that it is important to see its form. To simplify matters, we shall express it in terms of the ratio of the population of a state of energy E to the population of the lowest state, of energy 0:
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Specifically, β = 1/kT, where k is a fundamental constant called Boltzmann’s constant.
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To bring β into line with the Kelvin temperature scale, k has the value 1.38 × 10–23 joules per kelvin.1 The point to remember is that, because β is proportional to 1/T, as the temperature goes up, β goes down, and vice versa.
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First, the huge importance of the Boltzmann distribution is that it reveals the molecular significance of temperature: temperature is the parameter that tells us the most probable distribution of populations of molecules over the available states of a system at equilibrium.
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The second point is that β is a more natural parameter for expressing temperature than T itself.
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The third point is that the existence and value of the fundamental constant k is simply a consequence of our insisting on using a conventional scale of temperature rather than the truly fundamental scale based on β.
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the words ‘gas’ and ‘chaos’ stem from the same root),
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The Maxwell–Boltzmann distribution of molecular speeds for molecules of various mass and at different temperatures. Note that light molecules have higher average speeds than heavy molecules. The distribution has consequences for the composition of planetary atmospheres, as light molecules (such as hydrogen and helium) may be able to escape into space.
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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’.
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Work is the primary foundation of thermodynamics and in particular of the first law.
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the same amount of work, however it is performed, brings about the same change of state of the system. This conclusion is like climbing a mountain by a variety of different paths, each path corresponding to a different method of doing work.
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Provided we start at the same base camp and arrive at the same destination, we shall have climbed through the same height regardless of the path we took between them. That is, we can attach a number (the ‘altitude’) to every point on the mountain, and calculate the height we have climbed, regardless of the path, by taking the difference of the initial and final altitudes for our climb. Exactly the same applies to our system. The fact that the change of state is path-independent means that we can associate a number, which we shall call the internal energy (symbol U) with each state of the system.
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We have not yet arrived at the first law: this will take a little more work, both literally and figuratively.
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Typically, we find that more work has to be done than in the adiabatic case. We are driven to conclude that the internal energy can change by an agency other than by doing work. One way of regarding this additional change is to interpret it as arising from the transfer of energy from the system into the surroundings due to the difference in temperature caused by the work that we do as we churn the contents. This transfer of energy as a result of a temperature difference is called heat.
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The amount of energy that is transferred as heat into or out of the system can be measured very simply: we measure the work required to bring about a given change in the adiabatic system, and then the work required to bring about the same change of state in the diathermic system (the one with thermal insulation removed), and take the difference of the two values. That difference is the energy transferred as heat.
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In thermodynamics heat is not an entity or even a form of energy: heat is a mode of transfer of energy. It is not a form of energy, or a fluid of some kind, or anything of any kind. Heat is the transfer of energy by virtue of a temperature difference. Heat is the name of a process, not the name of an entity.
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The molecular distinction between the transfer of energy as work (left) and heat (right). Doing work results in the uniform motion of atoms in the surroundings; heating stimulates their disorderly motion.
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That is, heat is the transfer of energy that makes use of the random motion of atoms in the surroundings (Figure 8).
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The distinction between work and heat is made in the surroundings: the system has no memory of the mode of transfer nor is it concerned about how its store of energy will be used.
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That is, by ensuring that at every stage the expansion is reversible in the thermodynamic sense, the system does maximum work. This conclusion is general: reversible changes achieve maximum work.
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the leakage of energy from a system as work is automatically taken into account by focusing on the change in enthalpy. In other words, the enthalpy is the basis of a kind of accounting trick, which keeps track invisibly of the work that is done by the system, and reveals the amount of energy that is released only as heat, provided the system is free to expand in an atmosphere that exerts a constant pressure on the system.
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In former times, the extra energy of the vapour was termed the ‘latent heat’, because it was released when the vapour re-condensed to a liquid and was in some sense ‘latent’ in the vapour.