Treatise on Thermodynamics

Max Planck

• Publisher: Dover Publications
• Year: 2013
• eBook ISBN: 9780486319285
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Written by the founder of quantum theory, a Nobel Prize winner, this classic volume is still recognized as among the best introductions to thermodynamics. It is a model of conciseness and logic, ideally suited to the needs of both students and research workers in physics and chemistry.
Based on Planck's original papers, the book offers a uniform point of view for the entire field. Rejecting the earlier approaches of Helmholtz and Maxwell, Planck makes no assumptions regarding the nature of heat, but begins with only a few empirical facts from which he deduces new physical and chemical laws. He considers fundamental facts and definitions (temperature, molecular weight, quantity of heat), the first and second fundamental principles of thermodynamics (applications to homogeneous and non-homogeneous systems, proof, general deductions), and applications to special states of equilibrium (homogeneous systems, systems in various states of aggregation, system of any number of independent constituents, gaseous systems, dilute solutions, absolute value of the entropy, Nernst’s theorem). Throughout the book numerous examples are worked.

TREATISE

ON

THERMODYNAMICS.

PART I.

FUNDAMENTAL FACTS AND DEFINITIONS.

CHAPTER I.

TEMPERATURE.

§ 1. THE conception of “heat” arises from that particular sensation of warmth or coldness which is immediately experienced on touching a body. This direct sensation, however, furnishes no quantitative scientific measure of a body’s state with regard to heat; it yields only qualitative results, which vary according to external circumstances. For quantitative purposes we utilize the change of volume which takes place in all bodies when heated under constant pressure, for this admits of exact measurement. Heating produces in most substances an increase of volume, and thus we can tell whether a body gets hotter or colder, not merely by the sense of touch, but also by a purely mechanical observation affording a much greater degree of accuracy. We can also tell accurately when a body assumes a former state of heat.

§ 2. If two bodies, one of which feels warmer than the other, be brought together (for example, a piece of heated metal and cold water), it is invariably found that the hotter body is cooled, and the colder one is heated up to a certain point, and then all change ceases. The two bodies are then said to be in thermal equilibrium. Experience shows that such a state of equilibrium finally sets in, not only when two, but also when any number of differently heated bodies are brought into mutual contact. From this follows the important proposition : If a body, A, be in thermal equilibrium with two other bodies, B and C, then B and C are in thermal equilibrium with one another. For, if we bring A, B, and C together so that each touches the other two, then, according to our supposition, there will be equilibrium at the points of contact AB and AC, and, therefore, also at the contact BC. If it were not so, no general thermal equilibrium would be possible, which is contrary to experience.

§ 3. These facts enable us to compare the degree of heat of two bodies, B and C, without bringing them into contact with one another; namely, by bringing each body into contact with an arbitrarily selected standard body, A (for example, a mass of mercury enclosed in a vessel terminating in a fine capillary tube). By observing the volume of A in each case, it is possible to tell whether B and C are in thermal equilibrium or not. If they are not in thermal equilibrium, we can tell which of the two is the hotter. The degree of heat of A, or of any body in thermal equilibrium with A, can thus be very simply defined by the volume of A, or, as is usual, by the difference between the volume of A and an arbitrarily selected normal volume, namely, the volume of A when in thermal equilibrium with melting ice under atmospheric pressure. This volumetric difference, which, by an appropriate choice of unit, is made to read 100 when A is in contact with steam under atmospheric pressure, is called the temperature in degrees Centigrade with regard to A as thermometric substance. Two bodies of equal temperature are, therefore, in thermal equilibrium, and vice versâ.

§ 4. The temperature readings of no two thermometric substances agree, in general, except at 0° and 100° The definition of temperature is therefore somewhat arbitrary. This we may remedy to a certain extent by taking gases, in particular those hard to condense, such as hydrogen, oxygen, nitrogen, and carbon monoxide, and all so-called permanent gases as thermometric substances. They agree almost completely within a considerable range of temperature, and their readings are sufficiently in accordance for most purposes. Besides, the coefficient of expansion of these different gases is the same, inasmuch as equal volumes of them expand under constant pressure by the same amount—about

of their volume—when heated from 0° C. to 1° C. Since, also, the influence of the external pressure on the volume of these gases can be represented by a very simple law, we are led to the conclusion that these regularities are based on a remarkable simplicity in their constitution, and that, therefore, it is reasonable to define the common temperature given by them simply as temperature. We must consequently reduce the readings of other thermometers to those of the gas thermometer.

§ 5. The definition of temperature remains arbitrary in cases where the requirements of accuracy cannot be satisfied by the agreement between the readings of the different gas thermometers, for there is no sufficient reason for the preference of any one of these gases. A definition of temperature completely independent of the properties of any individual substance, and applicable to all stages of heat and cold, becomes first possible on the basis of the second law of thermodynamics (§ 160, etc.). In the mean time, only such temperatures will be considered as are defined with sufficient accuracy by the gas thermometer.

§ 6. In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface. They, therefore, also exert the same pressure outwards. Surface phenomena are thereby disregarded. The condition of such a body is determined by its chemical nature; its mass, M; its volume, V; and its temperature, t. On these must depend, in a definite manner, all other properties of the particular state of the body, especially the pressure, which is uniform throughout, internally and externally. The pressure, p, is measured by the force acting on the unit of area—in the c.g.s. system, in dynes per square centimeter, a dyne being the force which imparts to a mass of one gramme in one second a velocity of one centimeter per second.

§ 7. As the pressure is generally given in atmospheres, the value of an atmosphere in absolute C.G.S. units is here calculated. The pressure of an atmosphere is the force which a column of mercury at 0° C, 76 cm. high, and 1 sq. cm. in cross-section exerts on its base in consequence of its weight, when placed in geographical latitude 45°. This latter condition must be added, because the weight, i.e. the force of the earth’s attraction, varies with the locality. The volume of the column of ...

Table of contents

• Cover
• Title Page
• Copyright Page
• Authors’ Preface
• Editions Preface
• Contents
• Part I: Fundamental Facts and Definitions.
• Part II: The First Fundamental Principle of Thermodynamics
• Part III: The Second Fundamental Principle of Thermodynamics
• Part IV: Applications to Special States of Equilibrium
• Index