Chapter 1
Heat, Work, and Energy

1.1 INTRODUCTION

Thermodynamics is deceptively simple or exceedingly complex, depending on how you approach it. In this book, we will be concerned with the principles of thermodynamics that are especially useful in thinking about biological phenomena. The emphasis will be on concepts, with a minimum of mathematics. Perhaps an accurate description might be rigor without rigor mortis. This may cause some squirming in the graves of thermodynamic purists, but the objective is to provide a foundation for researchers in experimental biology to use thermodynamics. This includes cell biology, microbiology, molecular biology, and pharmacology, among others. A more advanced treatment of some aspects of thermodynamics is presented in Chapter 4. Excellent texts are available that present a more complete exposition of thermodynamics (cf. Refs. (1-3)).

In point of fact, thermodynamics can provide a useful way of thinking about biological processes and is indispensable when considering molecular and cellular mechanisms. For example, what reactions and coupled physiological processes are possible? What are the allowed mechanisms involved in cell division or in protein synthesis? What are the thermodynamic considerations that cause proteins, nucleic acids, and membranes to assume their active structures? It is easy to postulate biological mechanisms that are inconsistent with thermodynamic principles-but just as easy to postulate those that are consistent. Consequently, no active researcher in biology should be without a rudimentary knowledge of the principles of thermodynamics. The ultimate goal of this exposition is to understand what determines equilibrium in biological systems and how these equilibrium processes can be coupled together to produce living systems, even though we recognize that living organisms are not at equilibrium. Thermodynamics provides a unifying framework for diverse systems in biology. Both a qualitative and a quantitative understanding are important and will be developed.

The beauty of thermodynamics is that a relatively small number of postulates can be used to develop the entire subject. Perhaps the most important part of this development is to be very precise with regard to concepts and definitions, without getting bogged down with mathematics. Thermodynamics is a macroscopic theory, not molecular. As far as thermodynamics is concerned, molecules need not exist. However, we will not be purists in this regard: If molecular descriptions are useful for understanding or introducing concepts, they will be used. We will not hesitate to give molecular descriptions of thermodynamic results, but we should recognize that these interpretations are not inherent in thermodynamics itself. It is important to note, nevertheless, that large collections of molecules are assumed so that their behavior is governed by Boltzmann statistics; that is, the normal thermal energy distribution is assumed. This is almost always the case in practice. Furthermore, thermodynamics is concerned with time-independent systems, that is, systems at equilibrium. Thermodynamics has been extended to nonequilibrium systems, but we will not be concerned with the formal development of this subject here.

The first step is to define the system. A thermodynamic system is simply that part of the universe in which we are interested. The only caveat is that the system must be large relative to molecular dimensions. The system could be a room, it could be a beaker, it could be a cell, etc. An open system can exchange energy and matter across its boundaries, for example, a cell or a room with open doors and windows. A closed system can exchange energy but not matter, for example, a closed room or box. An isolated system can exchange neither energy nor matter, for example, the universe or, approximately, a closed Dewar flask. We are free to select the system as we choose, but it is very important that we specify what it is. This will be illustrated as we proceed. The properties of a system are any measurable quantities characterizing the system. Properties are either extensive, proportional to the amount of material in the system, or intensive, independent of the amount of material. Examples of extensive properties are mass and volume. Examples of intensive properties are temperature, pressure, and color.

1.2 TEMPERATURE

We are now ready to introduce three important concepts: temperature, heat, and work. None of these are unfamiliar, but we must define them carefully so that they can be used as we develop thermodynamics.

Temperature is an obvious concept, as it simply measures how hot or cold a system is. We will not belabor its definition and will simply assert that thermodynamics requires a unique temperature scale, namely, the Kelvin temperature scale. The Kelvin temperature scale is related to the more conventional Celsius temperature scale by the definition

Although the temperature on the Celsius scale is referred to as "degrees Celsius," by convention degrees are not stated on the Kelvin scale. For example, a temperature of 100 °C is 373 K. (Thermodynamics is entirely logical-some of the conventions used are not.) The definition of thermal equilibrium is very simple: When two systems are at the same temperature, they are at thermal equilibrium.

1.3 HEAT

Heat flows across the system boundary during a change in the state of the system because a temperature difference exists between the system and its surroundings. We know of many examples of heat: Some chemical reactions produce heat, such as the combustion of gas and coal. Reactions in cells can produce heat. By convention, heat flows from higher temperature to lower temperature. This fixes the sign of the heat change. It is important to note that this is a convention and is not required by any principle. For example, if the temperature of the surroundings decreases, heat flows to the system, and the sign of the heat change is positive (+). A simple example will illustrate this sign convention as well as the importance of defining the system under consideration.

Consider two beakers of the same size filled with the same amount of water. In one beaker, A, the temperature is 25 °C, and in the other beaker, B, the temperature is 75 °C. Let us now place the two beakers in thermal contact and allow them to reach thermal equilibrium (50 °C). This situation is illustrated in Figure 1-1. If the system is defined as A, the temperature of the system increases, so the heat change is positive. If the system is defined as B, the temperature of the system decreases, so the heat change is negative. If the system is defined as A and B, no heat flow occurs across the boundary of the system, so the heat change is zero! This illustrates how important it is to define the system before asking questions about what is occurring.

Figure 1-1 Illustration of the establishment of thermal equilibrium and importance of defining the system carefully. Two identical vessels filled with the same amount of liquid, but at different temperatures, are placed in contact and allowed to reach thermal equilibrium. A discussion of this figure is given in the text.

The heat change that occurs is proportional to the temperature difference between the initial and final states of the system. This can be expressed mathematically as

where q is the heat change, the constant C is the heat capacity, Tf is the final temperature, and Ti is the initial temperature. This relationship assumes that the heat capacity is constant, independent of the temperature. In point of fact, the heat capacity often changes as the temperature changes, so that a more precise definition puts this relationship in differential form:

Note that the heat change and the heat capacity are extensive properties-the larger the system, the larger the heat capacity and the heat change. Temperature, of course, is an intensive property.

1.4 WORK

The definition of work is not as simple as that for heat. Many different forms of work exist, for example, mechanical work, such as muscle action, and electrical work, such as ions crossing charged membranes. We will use a rather artificial, but very general, definition of work that is easily understood. Work is a quantity that can be transferred across the system boundary and can always be converted to lifting and lowering a weight in the surroundings. By convention, work done on a system is positive: this corresponds to lowering the weight in the surroundings.

You may recall that mechanical work, w, is defined as the product of the force in the direction of movement, Fx, times the distance moved, x, or in differential form

Therefore, the work to lower a weight is -mgh, where m is the mass, g is the gravitational constant, and h is the distance the weight is lowered. This formula is generally useful: for example, mgh is the work required for a person of mass m to walk up a hill of height h. The work required to stretch a muscle could be calculated with Eq. (1-4) if we knew the force required and the distance the muscle was stretched. Electrical work, for example, is equal to -EIt, where E is the...