179-181] Thermodynamics 159 



THERMODYNAMICS. 



Equation of Energy. 



180. The total energy of the gas may be divided into internal and 

 external. The former consists of the kinetic energy of molecular motion 

 and the potential energy of intermolecular forces. The external energy is 

 measured by the work which could be performed by the gas in expanding 

 to a state of infinite rarity starting from its present configuration, this 

 work of course being performed in opposition to the pressure of the gas. 

 The external energy will be denoted by 2B, the internal energy by (.. As in 

 equation (133) we have 



..................... (379), 



where E is the mean energy of the N molecules, and 3> is the potential 

 energy of the intermolecular forces. 



181. Let us suppose that a quantity d<& of energy, either in the form 

 of heat or otherwise, is absorbed by the gas from some external source, so that 

 as a consequence the pressure, volume and temperature of the gas change. 

 We shall suppose d(& measured in work-units; the corresponding quantity 

 measured in heat-units will be connected with d(& by the relation 



............................. (380), 



where / is the mechanical equivalent of heat. 



Let us suppose that after this absorption of heaj; the gas again assumes 

 a steady state, and that in the new state the values of 2B and (S have become 

 changed to 28 4- d$Q and ( + d(&. The energy equation obtained by 

 equating the total energies before and after the change is 



. ......... (381), 



..................... (382). 



If we suppose the volume of the gas increased, by a small element dS 

 of the surface moving a small distance dn parallel to itself normally outwards, 

 then obviously the work done by the gas will be that of moving a force pdS 

 through a distance dn. We therefore have 



The resulting increase in volume (dv) is of course the sum of the contri- 

 butions dSdn from all the elements of surface which are moved, so that 

 the equation becomes 



pdv ................................. (383). 



