162 Physical Properties [OH. vn 



so that tff c , as we should expect, is proportional to the b of Van der Waals, 

 being in fact a fraction - of the whole pressure. The internal pressure pi is 

 therefore given by 



a 



=^ + - 2 > 



in Van der Waals' equation. 



185. To calculate d<& we notice that when the gas expands or is 

 compressed, the pressure -57 C does not do any work, for the molecules 

 themselves do not expand or contract with the gas. To a first approxi- 

 mation, we may suppose that every element of the gas expands in the 

 same ratio, so that any element dxdydz expands to a volume (1 + e) dxdydz. 

 The resulting contribution to d$> is ^iedxdydz, the negative sign indicating 

 that work is done by the pressure on the gas, and not as before by the gas 

 against the pressure. The total value of d$> is accordingly 



6 dxdydz ........................ (389), 



or, using the value of T&i given by equation (387), 



d <b = .^l:_^ dv ........................ ( 390). 



The energy equation is now 



= NdE+pdv 



= NdE 



2h 



(391). 



The equation is therefore of exactly the same form as equation (385), 

 obtained on neglecting cohesion forces, but the value of 17, must be calculated 

 on the supposition of a uniform density p equal to the mean density of the 

 gas. This value of v b is of course a function only of the constants and 

 volume of the gas (cf. equation (293)). 



The First Law of Thermodynamics. 



186. The law which is commonly termed the first law of thermodynamics 

 is that contained in equation (380), and simply expresses that heat is energy, 

 which is capable of transformation into the kinetic energy of motion of 

 material masses. This, however, is all included in the hypothesis upon which 

 the Kinetic Theory is based. Thus, in the Kinetic Theory, the first law of 

 thermodynamics is reduced to a truism. 



