390 Thermodynamics and Biology /2I : 3 



approached zero, then the entropy change would approach minus 

 infinity when a body was cooled toward absolute zero. The third law 

 states that this is not true; that the entropy change remains finite. In 

 other words, the third law states that the specific heat of all substances 

 goes to zero at least as fast as the temperature in the neighborhood of 

 absolute zero. 



A somewhat stronger form of the third law states that the entropy 

 of all single crystals is the same at absolute zero and may be con- 

 veniently chosen as zero. This means, for example, that if one measures 

 the entropy changes for two moles of hydrogen and one of oxygen from 

 zero absolute to room temperature and adds the entropy due to the 

 formation of liquid water, then the final sum should be identical to the 

 entropy change from ice at 0°K to water at room temperature. This 

 stronger version of the third law has been verified for many substances 

 and never refuted for any substance tested. 



3. Other Thermodynamic Functions 



Three thermodynamic functions, other than the entropy, are more 

 satisfactory for discussing equilibrium conditions in nonisolated systems. 

 One of these is the enthalpy H defined by 



H = E + pV (8) 



In an isobaric system 1 , doing only pdV work 



dH = dE + pdV + Vdp = 8Q because dp = 



For this reason, the enthalpy is sometimes called the heat or heat function. 

 It should be clear that these names are misleading. 



The other two functions are both called free energy; one or the other 

 is designated by F in many texts. A less ambiguous approach is to use 

 A for the Helmholtz free energy defined by 



A = E - TS (9) 



and G for the Gibbs' free energy defined by 



G = H - TS (10) 



A little manipulation shows that 



dA = -SdT - 8W (11) 



and 



dG = -SdT + Vdp - W (12) 



1 Constant pressure. 



