CHAPTER VI. 



PHYSICAL PROPERTIES OF A GAS. 



PRESSURE, DENSITY AND TEMPERATURE. 



118. IN the preceding chapters the main dynamical problem of the 

 motion of a gas has been solved with sufficient generality to justify us in 

 hoping for some agreement with the results of experiment. We therefore 

 attempt now to interpret the mathematical results which have been obtained, 

 in terms of the physical properties of a gas. We shall begin by investigating 

 the law which ought, as a consequence of our mathematical analysis, to 

 connect the pressure, volume and temperature of a gas. 



Calculation of the Pressure of a Gas. 



119. Let us consider any small element dS of the surface of the vessel 

 containing the gas, this element being so small that it may, without appre- 

 ciable error, be regarded as plane. The directions of the axes are at present 

 perfectly arbitrary, so that we may choose them so that the outward normal 

 to dS is parallel to the axis of x. 



If p is the pressure per unit area at the element dS, the pressure on dS 

 is pdS, and therefore pdSdt is equal to the sum of the normal components 

 of the impulsive forces exerted upon dS by the various molecules which 

 enter into collision with it during the interval dt. If A is any such molecule, 

 the normal impulse exerted by A on dS may be divided into two parts I a arid 

 I a ', I a being the total normal impulse up to the moment at which the velocity 

 of the centre of gravity normal to the boundary dS is nil, and I a ' the -total 

 normal impulse from this moment up to the time at which the molecule A is 

 again clear of the boundary. If the velocities of the centre of gravity of A 

 before and after collision are 



u a , v a> w a and u a f , v a f , w a ', 

 we have 



