21 : 2/ Thermodynamics and Biology 389 



(For nonideal solutions, it is possible to define a dimensionless quantity 

 called the fugacity/such that 



W' c = J n.RTdilnf^ 



i= 1 



is correct. However, it will not be necessary to use f in the specific 

 topics considered in this text.) 



The first law of thermodynamics may be rewritten by combining 

 Equations 1 through 6 into the form 



dE = TdS - pdV + I ni RTd(ln c { ) - 2 FMx - 2 ^dq x (7) 



The last sum is biologically important at membranes, whereas the next 

 to last sum is significant in problems involving muscular contraction 

 or the elastic properties of tissues. In discussions of enzyme activity, 

 both of the last two sums may be set to zero. 



There are two other laws of thermodynamics, both of which may be 

 expressed in terms of the entropy. The second law of thermodynamics is 

 concerned with the direction of time. In all of mechanics and in 

 electricity and magnetism, there is nothing to distinguish the positive 

 and negative directions of time. The second law of thermodynamics 

 states essentially that the positive direction of time is that in which heat 

 flows from a hot body to a cold body in an isolated system. When a 

 given amount of heat 8Q leaves a body at 7\ and flows to a colder body 

 at T 2 , the net change of entropy 



,,8Q _ 8Q 

 T 2 T, 



is greater than zero. The second law of thermodynamics states that in 

 an isolated system the entropy will be a maximum at equilibrium. The 

 conditions for equilibrium of an isolated system then are 



dS = 



dE = 



d 2 S < 0, that is, S is a maximum 



Although it is mathematically useful to discuss isolated systems, tinw- 

 are as unreal as frictionless systems; no system is known which is com- 

 pletely thermodynamically isolated. In a real system, the entropy mux- 

 decrease with time. 



The third law of thermodynamics is a more recent invention than the 

 first and second laws. The third law is concerned with what happens 

 to the entropy as the absolute temperature approaches zero. Equation 2 

 shows that the definition of dS has a factor of 1 T. If the specific heat 

 of a substance remained greater than zero as the absolute temperature 



