IN LIVING MATTER 



21 



amount of volume energy appears dependent upon the pressure, 

 and as a result the heat produced will be less by this amount ; and 

 similarly when a grm. molecule disappears at another different 

 pressure, a definite amount of volume energy disappears, and by 

 this amount the heat of reaction will increase. Accordingly the 

 difference in these two amounts will express V, the change in 

 volume energy in the reaction. 



The difference in volume energy before and after the reaction 

 cannot be obtained by taking the differences in the total osmotic 

 pressures before and after the reaction, because the quantity of 

 substance appearing is not brought during the change from the 

 one of these pressures to the other, but from the zero of pressure 

 to the pressure at which it is finally found in the reaction, that 

 is, to the partial pressure of the component substance to which 

 it belongs ; and similarly the grm. molecule of substance 

 disappearing passes from the 

 partial pressure at which that 

 substance happens to be present 

 in solution to zero pressure. 

 Hence the amount of volume 

 energy must be obtained sepa- 

 rately for each substance taking 

 part in the reaction. 



This amount of energy may 

 be obtained as follows : Sup- 

 pose a definite amount of a sub- 

 stance to be in solution in a 

 semi -permeable cylinder fitted 

 with a semi-permeable piston, 

 as sketched in the diagram, and 

 surrounded by solvent. Then 

 if the pressure on the piston be FlG> i._Work done in Compression of a 

 changed, just as in the case of a Solution in a Semi-permeable Cylinder, 

 gas, the solution will correspond- 

 ingly change in volume. The work done by the dissolved substance or 

 solute is PtV, where P is the pressure and dV the small change in 

 the volume. Or, using the gas law PV = ET, we have on differentia- 



T? T* /7T* 



tion PdV = - VdP, and again since V = ^f, PdV = RT ~. On integ- 

 rating this yields for the work done by the gas in expanding isother- 



