386 Thermodynamics and Biology /2I :2 



physical discipline whose theory is expressed most readily in mathe- 

 matical terms. Because of this, and because the theory and applications 

 of thermodynamics are often found in separate courses, many students 

 receive a B.S. degree in physics or chemistry with little or no knowledge 

 of thermodynamics. 



Accordingly, the development of thermodynamics is included in this 

 chapter. No attempt has been made either to include rigorous proofs 

 or to eliminate the fundamentally mathematical symbolism involved. 

 Those terms and parts of thermodynamics of greatest application to 

 biology are emphasized, particularly the concepts of energy, entropy, 

 and Gibbs' free energy. The last-mentioned concept is applied in the 

 concluding sections of this chapter to a discussion of chemical equilibria. 

 This application has received the greatest attention by biologists; it is 

 one of the more important uses of thermodynamics in describing bio- 

 logical systems. 



2. The Laws of Thermodynamics 



Thermodynamics is a study of the exchange of heat between bodies 

 and of the conversion of heat to and from other forms of energy. Energy 

 is not something which we see or feel; it is a concept constructed by 

 humans to describe the external world. Energy is defined as the ability 

 to do mechanical work W. This in turn is defined as the product of a 

 force F exerted times the distance s moved in the direction of the force. 

 (In the language of integral calculus, this last statement becomes 



| 2 F-ds 



-r 



where W is the work done by F in moving from position 1 to 2 and the 

 arrows indicate vectors.) 



Mechanical energy may exist in two general forms, potential and 

 kinetic. Potential energy includes elastic energy and gravitational energy. 

 Sound or acoustic energy is a mixture of potential and kinetic energy. 

 In a frictionless system, mechanical energy would always be conserved. 

 Because friction occurs in all real systems, mechanical energy is lost. 

 Moreover, mechanical energy sources are also known, for example, 

 human beings, so that in a real system mechanical energy may be both 

 generated and dissipated. 



To physicists, the idea of conservation is a pleasing one. It was 

 proposed to retain the concept of conservation of mechanical energy even 

 in the presence of friction and heat driven machines, by including heat 

 as a form of energy. Joule proved experimentally that for every unit 



