Chapter 1: Temperature and the Zeroth Law of Thermodynamics PDF

## Chapter 1: Temperature and the Zeroth Law of Thermodynamics - **Dynamics includes, in addition to the above, such systems** - resistors, - electric capacitors, and - magnetic substances. ### 1.5 Thermal Equilibrium and the Zeroth Law - **We have seen that a macroscopic description...

## Chapter 1: Temperature and the Zeroth Law of Thermodynamics - **Dynamics includes, in addition to the above, such systems** - resistors, - electric capacitors, and - magnetic substances. ### 1.5 Thermal Equilibrium and the Zeroth Law - **We have seen that a macroscopic description of a gaseous mixture may be given by specifying such quantities as:** - the composition, - the mass, - the pressure, and - the volume. - **The last quantity specified in Sec. 1.1 was temperature, for which you have an intuitive understanding and some familiarity.** - **This section begins the analytic development of the quantity, temperature.** - **Experiment shows that, for a given composition and for a constant mass and temperature, many different values of pressure and volume are possible for a gas.** - **If the pressure is kept constant, the volume may vary over a wide range of values, and vice versa.** - **In other words, the pressure and the volume are independent coordinates but are related in a simple equation, namely, Boyle's law.** - **More recently, experiment has shown that, for a wire of constant mass, the tension and the length are independent coordinates, whereas, in the case of a surface film, the surface tension and the area may be varied independently.** - **Some systems that, at first sight, seem quite complicated, such as an electric cell with two different electrodes and an electrolyte, may still be described with the aid of only two independent coordinates.** - **On the other hand, some thermodynamic systems composed of a number of homogeneous parts require the specification of two independent coordinates for each homogeneous part.** - **Details of various thermodynamic systems and their thermodynamic coordinates will be given in Chap. 2.** - **For the present, to simplify our discussion, we shall deal only with systems of constant mass and composition, each requiring only one pair of independent coordinates for its description.** - **This involves no essential loss of generality and results in a considerable saving of words.** - **In referring to any unspecified system, we shall use the symbols X and Y for the pair of independent coordinates, where the symbol X refers to a generalized force (for instance, the pressure of a gas) and Y refers to a generalized displacement (for instance, the volume of a gas).** - **A state of a system in which the coordinates X and Y have definite values that remain constant so long as the external conditions are unchanged is called an equilibrium state.** - **Experiment shows that the existence of an equilibrium state in one system depends on the proximity of other systems and on the nature of the boundary or wall separating the different systems.** - **Walls are said to be either adiabatic or diathermic in ideal cases.** - **If a wall is adiabatic [see Fig. an equilibrium state for system A may coexist with any equilibrium state of system B for all attainable values of the four quantities, X, Y and X', Y' provided only that the wall is able to withstand the stress associated with the difference between the two sets of coordinates.** - **Thick layers of wood, concrete, asbestos, felt, or polystyrene, as well as dewars, are, in this order, increasingly better experimental approximations to ideal adiabatic walls.** ### 6 Part 1: Fundamental Concepts: - In other words, when we seek to understand the physical reality of a result of a microscopic calculation, we look to the macroscopic point of view for guidance. ### 1.4 Scope of Thermodynamics - **It has been emphasized that a description of the large-scale characteristics of a system by means of a few of its measurable properties, suggested more or less directly by our sensory perceptions, constitutes a macroscopic description.** - **Such descriptions are the historic starting point of all investigations in all branches of natural science.** - **For example, in dealing with the mechanics of a rigid body, we adopt the macroscopic point of view in that only the external aspects of the rigid body are considered.** - **The position of its center of mass is specified with reference to coordinate axes at a particular time.** - **Position and time and a combination of both, such as velocity, constitute some of the macroscopic quantities used in classical mechanics and are called mechanical coordinates.** - **The mechanical coordinates serve to determine the potential and the kinetic energy of the rigid body with reference to the coordinate axes, namely, the kinetic and the potential energy of the body as a whole.** - **These two types of energy constitute the external, or mechanical, energy of the rigid body.** - **It is the purpose of mechanics to find such relations between the position coordinates and the time as are consistent with Newton's laws of motion.** - **In thermodynamics, however, the attention is directed to the interior of a system.** - **A macroscopic point of view is adopted, and emphasis is placed on those macroscopic quantities which have a bearing on the internal state of a system.** - **It is the function of experiment to determine the quantities that are appropriate for a description of such an internal state.** - **Macroscopic quantities, including temperature, having a bearing on the internal state of a system are lied thermodynamic coordinates.** - **Such coordinates serve to determine the internal energy of a system.** - **It is the purpose of thermodynamics to find among the thermodynamic coordinates, general relations that are consistent** - **A system that may be described in terms of thermodynamic coordinates is e important thermodynamic systems are a gas, such as air; a vapor, such as steam, a mixture, such and in addition, aporized with freon. reactions, Chemical surface thermodynamics films, and electric deals with cells these, such as iiquidand** ### 8 Part 1: Fundamental Concepts: - [Diagram of Adiabatic and Diathermic walls] - **Properties of (a) adiabatic and (b) diathermic walls.** - **If the two systems are separated by a diathermic wall [see Fig. I-I (b)], the values of X, Y and x 1, Y' will change spontaneously until an equilibrium state of the combined system is attained.** - **The two systems are then said to be in thermal equilibrium with each other.** - **The most common experimental diathermic wall is a thin metallic sheet.** - **Thermal equilibrium is the state achieved by two (or more) systems, characterized by restricted values of the coordinates of the systems, after they have been in communication with each other through a diathermic wall.** - **Unlike the diathermic wall, an adiabatic wall prevents two systems from communicating with each other and coming to thermal equilibrium with each other.** - **Although we have not yet defined the concept of heat, it may be said that a diathermic wall is a boundary through which heat is communicated from one system to another system, yet remains closed to the transport of matter.** - **An ideal adiabatic wall does not communicate heat.** - **Imagine two systems A and B, separated from each other by an adiabatic wall but each in contact simultaneously with a third system C through diathermic walls, the whole assembly being surrounded by an adiabatic wall as shown in Fig. I-2(a).** - **Experiment shows that the two systems will come to their thermal equilibrium with the third system.** - **No further change will occur if the adiabatic wall separating A and B is then replaced by a diathermic wall, as well as if the diathermic wall separating C from both A and B is also replaced by an adiabatic wall [Fig. If, instead of allowing both systems A and B to come to equilibrium with C at the same time, we first establish equilibrium between A and C and later establish equilibrium between B and C (the state of system C being the same in both cases); then, when A and B are brought into communication through a diathermie wall, they will be found to be in thermal equilibrium with each other.** - **We shall use the expression "two systems are in thermal equilibrium" to mean also that the two systems are in states such that, if the two were connected through a diathermic wall, the combined system would be in thermal equilibrium.** ### The zeroth law of thermodynamics - **These experimental facts may then be stated concisely in the following transitive relation: Two systems in thermal equilibrium with a third are in thermal equilibrium with each other.** - **As suggested by Ralph Fowler, this postulate of transitive thermal equilibrium has been numbered the zeroth" law of thermodynamics, which establishes the basis for the concept of temperature and for the use of thermometers.** - **The postulate of thermal equilibrium is numbered the zeroth law, rather than the first law, because of the historical development in the understanding of the logical order of the laws of thermodynamics.** - **The first law of thermodynamics, which establishes the conservation of energy, including heat, was clearly formulated in 1848 by Hermann Helmholtz and William Thomson (later Lord Kelvin) using experimental data gathered by James Prescott Joule (1843-1849) and insight provided by Julius Mayer (1842).** - **The second law of thermodynamics was postulated earlier (1824) in Sadi Carnot's study of the working of steam engines.** - **Logically, Carnot's principle must follow the first law if his principle is expressed as a restriction on the means by which energy can be communicated while still being conserved.** - **As these postulates of thermodynamics were developed further, it was realized by ler (1931) that thermal equilibrium had to be defined before the first law could be stated.** - **Unable to renumber the two previously established laws of thermodynamics, he was forced to adopt zero as the number of his law.** - **It is unlikely that future developments will raise the possibility of the "minus first" law of thermodynamics.**