Chap Concepts And Definitions

1.1 A brief history of thermodynamics 1

1.1.1 The concept of temperature 1

1.1.3 Carnot and the foundations of the 2nd law 5

1.1.4 The First law and energy 7

1.1.5 Entropy and The 2nd Law of Thermodynamics 8

1.1.6 Gibbs and chemical thermodynamics 9

1.1.7 Historical summary 10

1.2 Thermodynamic nomenclature 11

1.3 Heat and work 13

1.4 Characteristics of system boundaries 14

1.5 Thermodynamic Processes 15

1.6 Thermodynamic Properties 17

1.6.1 Types of properties 17

1.6.2 Absolute Vs Relative Properties 18

1.7 Reversibile and Irreversibile processes 20

1.8 The First Law of Thermodynamics 25

1.9 The Second Law of Thermodynamics 29.

1.10 The fundamental differentials 35

1.11 Equilibrium 36

1.11.1 Internal equilibrium 36

1.11.2 External equilibrium 38

1.12 Components, Phases, and the Gibbs Phase Rule 38

1.12.1 One-componentsystems 39

1.12.2 Two-component systems 39

1.12.3 Counting components 40

1.12.4 Proof of the phase rule 41

References 43

1.1 A Brief History of Thermodynamics

The driving force for the development of thermodynamics was the invention of the steam engine around 1700. From 1700 to 1900, thermodynamic theory was slowly and fitfully developed. By 1900, "classical" thermodynamics was essentially complete. In time, various specialized branches of thermodynamics developed.

1.1.1 The Concept of Temperature

Qualitatively, temperature characterizes an object as hot, cold, warm, etc. Galileo (ca 1610) is said to have quantified temperature by the height of liquid in a vertical tube that extended into a pool of the liquid. The tube terminated at the top in a large air-filled glass bulb, which served as the temperature sensor. Such a device was suitable only for measuring changes in ambient air temperature. A major advance was made by the instrument-maker Fahrenheit who in 1724 constructed the earliest version of the mercury thermometer, descendants of which exist to this day. Because of its compactness and unitary construction in a single piece of glass, Fahrenheit's thermometer could be inserted into a liquid, or into orifices of the human body. By adjusting the quantity of ordinary sea salt in an ice-water mixture, the lowest temperature attained was fixed at 0o on the Fahrenheit scale1. By placing the thermometer in his mouth, he decreed a temperature of 96oF. The mercury column responded linearly to other temperatures. For example, when inserted into boiling water, the mercury column rose to 2.21 times the rise at the bodily reference point of 96oF (both with respect to the 0oF position). Thus, the boiling point of pure water is 212oF. In similar fashion, the temperature of an ice-water mixture (without salt) is 32oF.

Celsius (1742) defined 0oC as the boiling point of water and 100oC as the melting point of ice. Soon thereafter, Linnaeus reversed these designations and divided the intervening scale into 100 parts, giving rise to the centigrade scale. With only minor differences, the centigrade scale morphed into the Celsius scale, which, however, has been given a much sounder fundamental basis than simply relying on the two phase changes of water.

The first of the fundamental characterizations of the temperature scale is based on the notion of the absolute zero temperature, introduced by Kelvin (ca 1885). This reference mark can be determined by the version of Galileo's gas thermometer shown in Fig. 1.1. The square vessel of volume V contains n moles of an ideal gas, which obeys the law:

where p is the pressure of the gas in the vessel and R is a constant. Being part of what is in fact a thermodynamic relation, the temperature T in the ideal gas law must have a fundamental meaning that is not captured by the arbitrary Celsius scale. The objective of the experiment shown in Fig. 1.1 is to relate the "thermodynamic" temperature in the above equation to the Celsius temperature.

1 The topic of freezing-point depression, as illustrated by salt/ice/water mixtures, is treated in Chap. 9

In the experiment, the pressure is measured as a function of the gas temperature, which is fixed by the bath surrounding the vessel. In Fig. 1.1, ice/water is represented as the thermal medium, and the temperature assigned a value of 0 on the Celsius scale. Changing the temperature by using boiling water or dry ice as the thermal reservoir and measuring the gas pressure for each produces a straight-line plot on the T-p graph shown on the right-hand side of the figure. Points on this line are independent of the gas used, to the extent that it behaves ideally. The line in Fig. 1.1 is of the form ToC = Ap + T0, with the experimental intercept being -273 oC. A new temperature unit called the Kelvin, with a different zero than the Celsius scale but one degree the same in both, is defined by T(K) = ToC + 273.

In addition to the intercept, the slope of the line in Fig. 1.1 is nR/V. With n and V known, R is 82 cm3-atm/mole-K. Different units for pressure and volume give different values of R; however, the temperature units must remain Kelvins. R is called the universal gas constant, because it is independent of the gas used, always with the proviso that it behaves ideally. Since the units of pressure times volume are the same as force times distance, or energy, R can be converted to 1.986 calories/mole-K or 8.314 Joules/mole-K.

Use of the usual melting point of water as the zero reference for the Celsius scale is not sufficient for a quantity as fundamental as temperature. For instance, ice melts at a slightly higher temperature in Denver than in New York City. This difference is due to the effect of total pressure (exerted by the air) on the melting point2. To avoid this difficulty, an international committee has recently decreed that the reference state be that in which solid, liquid and gaseous water coexist in the absence of air or any other gas. Such a state defines the triple point, which for water is designated as 0.01 oC (273.16 K), where the vapor pressure is 0.00611 atm. The specification of the triple-point temperature as 0.01oC means that melting point of ice under atmospheric pressure remains 0oC or 273.15 K.

2 discussed in Chap. 5

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